See integral in All languages combined, or Wiktionary
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}, { "args": { "1": "en", "2": "la", "3": "integer", "t": "entire" }, "expansion": "Latin integer (“entire”)", "name": "der" } ], "etymology_text": "Borrowed from Middle French integral, from Medieval Latin integrālis, from Latin integer (“entire”); see integer.", "forms": [ { "form": "more integral", "tags": [ "comparative" ] }, { "form": "most integral", "tags": [ "superlative" ] } ], "head_templates": [ { "args": {}, "expansion": "integral (comparative more integral, superlative most integral)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "related": [ { "_dis1": "0 0 0 0 0 0 0 0 0 0", "word": "integer" }, { "_dis1": "0 0 0 0 0", "word": "integrity" }, { "_dis1": "0 0 0 0 0", "tags": [ "rare" ], "word": "integrous" } ], "senses": [ { "categories": [ { "_dis": "15 2 3 3 10 13 17 13 12 12", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": 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"parents": [], "source": "w+disamb" }, { "_dis": "14 2 2 2 11 12 18 13 11 15", "kind": "other", "name": "Terms with Ukrainian translations", "parents": [], "source": "w+disamb" }, { "_dis": "14 2 2 2 11 12 18 13 11 15", "kind": "other", "name": "Terms with Vietnamese translations", "parents": [], "source": "w+disamb" } ], "examples": [ { "ref": "1692–1717, Robert South, Twelve Sermons Preached upon Several Occasions, volume (please specify |volume=I to VI), London:", "text": "Ceasing to do evil, and doing good, are the two great integral parts that complete this duty.", "type": "quote" } ], "glosses": [ "Constituting a whole together with other parts or factors; not omittable or removable" ], "id": "en-integral-en-adj-2mBjIkgK", "links": [ [ "Constituting", "constitute" ], [ "whole", "whole" ], [ "part", "part" ], [ "factor", "factor" ], [ "omittable", "omittable" ], [ "removable", "removable" ] ], "synonyms": [ { "word": "immanent" }, { "word": "inherent" }, { "word": "necessary" }, { "word": "intrinsic" } ], "translations": [ { "_dis1": "78 0 0 1 20", "code": "ba", "lang": "Bashkir", "roman": "ayırılğıhıź", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "айырылғыһыҙ" }, { "_dis1": "78 0 0 1 20", "code": "bg", "lang": "Bulgarian", "roman": "nerazdelen", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "неразделен" }, { "_dis1": "78 0 0 1 20", "code": "bg", "lang": "Bulgarian", "roman": "cjalosten", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "цялостен" }, { "_dis1": "78 0 0 1 20", "code": "yue", "lang": "Chinese Cantonese", "roman": "jyun⁴ zing² ge³", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "完整嘅" }, { "_dis1": "78 0 0 1 20", "code": "cmn", "lang": "Chinese Mandarin", "roman": "wánzhěng de", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "完整的" }, { "_dis1": "78 0 0 1 20", "code": "cs", "lang": "Czech", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "nedílný" }, { "_dis1": "78 0 0 1 20", "code": "nl", "lang": "Dutch", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "integraal" }, { "_dis1": "78 0 0 1 20", "code": "eo", "lang": "Esperanto", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "integra" }, { "_dis1": "78 0 0 1 20", "code": "fi", "lang": "Finnish", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "olennainen" }, { "_dis1": "78 0 0 1 20", "code": "fi", "lang": "Finnish", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "kokonaisuuteen kuuluva" }, { "_dis1": "78 0 0 1 20", "code": "de", "lang": "German", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "integral" }, { "_dis1": "78 0 0 1 20", "code": "de", "lang": "German", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "ein Ganzes ausmachend" }, { "_dis1": "78 0 0 1 20", "code": "de", "english": "descriptive", "lang": "German", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "zur Erhaltung des Ganzen unentbehrlich" }, { "_dis1": "78 0 0 1 20", "code": "el", "lang": "Greek", "roman": "anapóspastos", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "αναπόσπαστος" }, { "_dis1": "78 0 0 1 20", "code": "he", "lang": "Hebrew", "roman": "integráli", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "אִינְטֶגְרָלִי" }, { "_dis1": "78 0 0 1 20", "code": "kk", "lang": "Kazakh", "roman": "integraldy", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "интегралды" }, { "_dis1": "78 0 0 1 20", "code": "kk", "lang": "Kazakh", "roman": "integraldyq", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "интегралдық" }, { "_dis1": "78 0 0 1 20", "code": "km", "lang": "Khmer", "roman": "dael teang srong", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "ដែលទាំងស្រុង" }, { "_dis1": "78 0 0 1 20", "code": "gv", "lang": "Manx", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "slane" }, { "_dis1": "78 0 0 1 20", "code": "pl", "lang": "Polish", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "jednolity" }, { "_dis1": "78 0 0 1 20", "code": "pl", "lang": "Polish", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "integralny" }, { "_dis1": "78 0 0 1 20", "code": "pt", "lang": "Portuguese", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "integral" }, { "_dis1": "78 0 0 1 20", "code": "ro", "lang": "Romanian", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "integral" }, { "_dis1": "78 0 0 1 20", "code": "ru", "lang": "Russian", "roman": "neotʺjémlemyj", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "неотъе́млемый" }, { "_dis1": "78 0 0 1 20", "code": "ru", "lang": "Russian", "roman": "nedelímyj", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "недели́мый" }, { "_dis1": "78 0 0 1 20", "code": "ru", "lang": "Russian", "roman": "neotdelímyj", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "неотдели́мый" }, { "_dis1": "78 0 0 1 20", "code": "sv", "lang": "Swedish", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "hel" }, { "_dis1": "78 0 0 1 20", "code": "sv", "lang": "Swedish", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "enhetlig" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "Of, pertaining to, or being an integer." ], "id": "en-integral-en-adj-hypLjVmH", "links": [ [ "mathematics", "mathematics" ], [ "integer", "integer" ] ], "raw_glosses": [ "(mathematics) Of, pertaining to, or being an integer." ], "topics": [ "mathematics", "sciences" ], "translations": [ { "_dis1": "7 43 25 22 3", "code": "ar", "lang": "Arabic", "roman": "takāmul", "sense": "math: of, pertaining to, or being an integer", "tags": [ "masculine" ], "word": "تَكَامُل" }, { "_dis1": "7 43 25 22 3", "code": "ba", "lang": "Bashkir", "roman": "bötön hanlı", "sense": "math: of, pertaining to, or being an integer", "word": "бөтөн һанлы" }, { "_dis1": "7 43 25 22 3", "code": "cs", "lang": "Czech", "sense": "math: of, pertaining to, or being an integer", "word": "celočíselný" }, { "_dis1": "7 43 25 22 3", "code": "nl", "lang": "Dutch", "sense": "math: of, pertaining to, or being an integer", "word": "geheel" }, { "_dis1": "7 43 25 22 3", "code": "eo", "lang": "Esperanto", "sense": "math: of, pertaining to, or being an integer", "word": "entjera" }, { "_dis1": "7 43 25 22 3", "code": "fi", "lang": "Finnish", "sense": "math: of, pertaining to, or being an integer", "word": "kokonaisluku-" }, { "_dis1": "7 43 25 22 3", "code": "fr", "lang": "French", "sense": "math: of, pertaining to, or being an integer", "word": "intégral" }, { "_dis1": "7 43 25 22 3", "code": "de", "lang": "German", "sense": "math: of, pertaining to, or being an integer", "word": "ganzzahlig" }, { "_dis1": "7 43 25 22 3", "code": "el", "lang": "Greek", "roman": "akéraios", "sense": "math: of, pertaining to, or being an integer", "tags": [ "masculine" ], "word": "ακέραιος" }, { "_dis1": "7 43 25 22 3", "code": "kk", "lang": "Kazakh", "roman": "integraldy", "sense": "math: of, pertaining to, or being an integer", "word": "интегралды" }, { "_dis1": "7 43 25 22 3", "code": "kk", "lang": "Kazakh", "roman": "integraldyq", "sense": "math: of, pertaining to, or being an integer", "word": "интегралдық" }, { "_dis1": "7 43 25 22 3", "code": "gv", "lang": "Manx", "sense": "math: of, pertaining to, or being an integer", "word": "slane-earrooagh" }, { "_dis1": "7 43 25 22 3", "code": "pt", "lang": "Portuguese", "sense": "math: of, pertaining to, or being an integer", "word": "inteiro" }, { "_dis1": "7 43 25 22 3", "code": "ro", "lang": "Romanian", "sense": "math: of, pertaining to, or being an integer", "word": "integral" }, { "_dis1": "7 43 25 22 3", "code": "ru", "lang": "Russian", "roman": "celočíslennyj", "sense": "math: of, pertaining to, or being an integer", "word": "целочи́сленный" }, { "_dis1": "7 43 25 22 3", "code": "es", "lang": "Spanish", "sense": "math: of, pertaining to, or being an integer", "word": "entero" }, { "_dis1": "7 43 25 22 3", "code": "sv", "lang": "Swedish", "sense": "math: of, pertaining to, or being an integer", "word": "compounds with heltal" }, { "_dis1": "7 43 25 22 3", "code": "tl", "lang": "Tagalog", "sense": "math: of, pertaining to, or being an integer", "word": "buumbilangin" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "Relating to integration (“the process of finding the integral [noun] of a function”)." ], "id": "en-integral-en-adj-W0p7Idnu", "links": [ [ "mathematics", "mathematics" ], [ "integration", "integration#English" ], [ "integral [noun", "integral#Noun" ], [ "function", "function" ] ], "raw_glosses": [ "(mathematics) Relating to integration (“the process of finding the integral [noun] of a function”)." ], "topics": [ "mathematics", "sciences" ], "translations": [ { "_dis1": "6 10 68 15 2", "code": "bg", "lang": "Bulgarian", "roman": "integralen", "sense": "math: relating to integration", "word": "интегрален" }, { "_dis1": "6 10 68 15 2", "code": "eo", "lang": "Esperanto", "sense": "math: relating to integration", "word": "integrala" }, { "_dis1": "6 10 68 15 2", "code": "fi", "lang": "Finnish", "sense": "math: relating to integration", "word": "integraali-" }, { "_dis1": "6 10 68 15 2", "code": "fr", "lang": "French", "sense": "math: relating to integration", "word": "intégral" }, { "_dis1": "6 10 68 15 2", "code": "kk", "lang": "Kazakh", "roman": "integraldy", "sense": "math: relating to integration", "word": "интегралды" }, { "_dis1": "6 10 68 15 2", "code": "kk", "lang": "Kazakh", "roman": "integraldyq", "sense": "math: relating to integration", "word": "интегралдық" }, { "_dis1": "6 10 68 15 2", "code": "es", "lang": "Spanish", "sense": "math: relating to integration", "word": "integral" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Algebra", "orig": "en:Algebra", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "Being the root of some monic polynomial in A." ], "id": "en-integral-en-adj-JhLlSgIy", "links": [ [ "algebra", "algebra" ], [ "commutative algebra", "commutative algebra" ], [ "ring", "ring" ], [ "element", "element" ], [ "subring", "subring" ], [ "root", "root" ], [ "monic", "monic" ], [ "polynomial", "polynomial" ] ], "qualifier": "commutative algebra", "raw_glosses": [ "(algebra, commutative 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Denoted using a long s: ∫, or a variant thereof.", "Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc." ], "id": "en-integral-en-noun-ph7r4pW~", "links": [ [ "mathematics", "mathematics" ], [ "operations", "operations" ], [ "calculus", "calculus" ], [ "differentiation", "differentiation" ], [ "function", "function" ], [ "displacement", "displacement" ], [ "area", "area" ], [ "volume", "volume" ], [ "infinitesimal", "infinitesimal" ], [ "limiting", "limit" ], [ "sequence", "sequence" ], [ "partial sum", "partial sum" ], [ "long s", "long s" ], [ "∫", "∫" ], [ "analytic", "analysis" ], [ "formalization", "formalization" ], [ "Riemann integral", "Riemann integral" ], [ "Lebesgue integral", "Lebesgue integral" ] ], "raw_glosses": [ "(mathematics) One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. 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diverges. In notation, #x5C;int#x5F;#x5C;frac#x7B;1#x7D;#x7B;2#x7D;¹#x5C;frac#x7B;1#x7D;#x7B;x#x7D;dx#x3D;#x5C;ln(2), but #x5C;int#x5F;0¹#x5C;frac#x7B;1#x7D;#x7B;x#x7D;dx#x3D;#x5C;infty.", "type": "example" }, { "text": "Stokes' theorem relates the integral over a surface of the curl of a vector field to a line integral around the boundary of that surface: #x5C;int#x5F;S#x5C;nabla#x5C;times#x5C;mathbf#x7B;F#x7D;#x5C;cdotd#x5C;mathbf#x7B;S#x7D;#x3D;#x5C;int#x5F;#x7B;#x5C;partialS#x7D;#x5C;mathbf#x7B;F#x7D;#x5C;cdotd#x5C;mathbf#x7B;r#x7D;,.", "type": "example" } ], "glosses": [ "A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of the integrand (or, generally, differential form) appearing in front of the integral sign." ], "id": "en-integral-en-noun-RVlHYzKc", "links": [ [ "mathematics", "mathematics" ], [ "definite integral", "definite integral" ], [ "application", "application" ], [ "subset", "subset" ], [ "domain", "domain" ], [ "number", "number" ], [ "positive", "positive" ], [ "negative", "negative" ], [ "infinity", "infinity" ], [ "finite", "finite" ], [ "converge", "converge" ], [ "diverge", "diverge" ], [ "interval", "interval" ], [ "integrand", "integrand" ], [ "differential form", "differential form" ] ], "raw_glosses": [ "(mathematics) A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of the integrand (or, generally, differential form) appearing in front of the integral sign." ], "topics": [ "mathematics", "sciences" ] }, { "antonyms": [ { "word": "derivative" } ], "categories": [ { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "15 2 3 3 10 13 17 13 12 12", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "14 1 4 2 9 13 17 13 11 15", "kind": "other", "name": "English heteronyms", "parents": [], "source": "w+disamb" }, { "_dis": "17 1 1 1 11 11 20 14 13 13", "kind": "other", "name": "Entries with 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{ "_dis": "14 2 2 2 10 12 17 15 11 15", "kind": "other", "name": "Terms with Serbo-Croatian translations", "parents": [], "source": "w+disamb" }, { "_dis": "15 1 2 2 10 14 18 14 11 13", "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w+disamb" }, { "_dis": "14 2 2 2 11 12 18 13 11 15", "kind": "other", "name": "Terms with Sundanese translations", "parents": [], "source": "w+disamb" }, { "_dis": "16 2 2 2 11 11 16 14 12 14", "kind": "other", "name": "Terms with Swedish translations", "parents": [], "source": "w+disamb" }, { "_dis": "14 2 2 2 10 12 17 15 11 15", "kind": "other", "name": "Terms with Tagalog translations", "parents": [], "source": "w+disamb" }, { "_dis": "14 2 2 2 10 12 18 13 11 16", "kind": "other", "name": "Terms with Thai translations", "parents": [], "source": "w+disamb" }, { "_dis": "14 2 2 2 10 12 17 15 11 15", "kind": "other", "name": "Terms with Turkish translations", "parents": [], "source": "w+disamb" }, { "_dis": "14 2 2 2 11 12 18 13 11 15", "kind": "other", "name": "Terms with Ukrainian translations", "parents": [], "source": "w+disamb" }, { "_dis": "14 2 2 2 11 12 18 13 11 15", "kind": "other", "name": "Terms with Vietnamese translations", "parents": [], "source": "w+disamb" }, { "_dis": "8 3 4 5 13 12 15 10 9 22", "kind": "topical", "langcode": "en", "name": "Calculus", "orig": "en:Calculus", "parents": [ "Mathematical analysis", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w+disamb" }, { "_dis": "8 3 4 5 13 12 15 10 9 22", "kind": "topical", "langcode": "en", "name": "Functions", "orig": "en:Functions", "parents": [ "Algebra", "Calculus", "Geometry", "Mathematical analysis", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w+disamb" } ], "glosses": [ "An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;", "The fluent of a given fluxion in Newtonian calculus." ], "id": "en-integral-en-noun-33mxjsHp", "links": [ [ "mathematics", "mathematics" ], [ "indefinite integral", "indefinite integral" ], [ "indefinite", "indefinite" ], [ "antiderivative", "antiderivative" ], [ "fluent", "fluent" ], [ "fluxion", "fluxion" ], [ "Newtonian", "Newtonian" ] ], "raw_glosses": [ "(mathematics) An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;", "(mathematics, historical or obsolete) The fluent of a given fluxion in Newtonian calculus." ], "synonyms": [ { "word": "antiderivative" }, { "word": "indefinite integral" }, { "word": "∫" } ], "tags": [ "historical", "obsolete" ], "topics": [ "mathematics", "sciences" ] } ], "sounds": [ { "enpr": "ĭnʹtĭ-grəl", "tags": [ "UK" ] }, { "ipa": "/ˈɪntɪɡɹ(ə)l/", "tags": [ "UK" ] }, { "enpr": "ĭnʹtə-grəl", "tags": [ "US" ] }, { "ipa": "/ˈɪntəɡɹəl/", "tags": [ "US" ] }, { "ipa": "/ɪnˈtɛɡɹəl/", "tags": [ "US" ] }, { "audio": "en-uk-integral-noun.ogg", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/b/bc/En-uk-integral-noun.ogg/En-uk-integral-noun.ogg.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/b/bc/En-uk-integral-noun.ogg" } ], "translations": [ { "_dis1": "34 34 8 9 15", "code": "hy", "lang": "Armenian", "roman": "integral", "sense": "limit of sums", "word": "ինտեգրալ" }, { "_dis1": "34 34 8 9 15", "code": "be", "lang": "Belarusian", "roman": "intehrál", "sense": "limit of sums", "tags": [ "masculine" ], "word": "інтэгра́л" }, { "_dis1": "34 34 8 9 15", "code": "bg", "lang": "Bulgarian", "roman": "integrál", "sense": "limit of sums", "tags": [ "masculine" ], "word": "интегра́л" }, { "_dis1": "34 34 8 9 15", "code": "ca", "lang": "Catalan", "sense": "limit of sums", "tags": [ "feminine" ], "word": "integració" }, { "_dis1": "34 34 8 9 15", "code": "yue", "lang": "Chinese Cantonese", "sense": "limit of sums", "word": "積分" }, { "_dis1": "34 34 8 9 15", "code": "yue", "lang": "Chinese Cantonese", "roman": "zik¹ fan¹", "sense": "limit of sums", "word": "积分" }, { "_dis1": "34 34 8 9 15", "code": "hak", "lang": "Hakka Chinese", "sense": "limit of sums", "word": "chit-fûn-ho̍k" }, { "_dis1": "34 34 8 9 15", "code": "cmn", "lang": "Chinese Mandarin", "sense": "limit of sums", "word": "積分" }, { "_dis1": "34 34 8 9 15", "code": "cmn", "lang": "Chinese Mandarin", "roman": "jī fēn", "sense": "limit of sums", "word": "积分" }, { "_dis1": "34 34 8 9 15", "code": "cs", "lang": "Czech", "sense": "limit of sums", "tags": [ "masculine" ], "word": "integrál" }, { "_dis1": "34 34 8 9 15", "code": "nl", "lang": "Dutch", "sense": "limit of sums", "word": "integraal" }, { "_dis1": "34 34 8 9 15", "code": "eo", "lang": "Esperanto", "sense": "limit of sums", "word": "integralo" }, { "_dis1": "34 34 8 9 15", "code": "eo", "lang": "Esperanto", "sense": "limit of sums", "word": "integro" }, { "_dis1": "34 34 8 9 15", "code": "fi", "lang": "Finnish", "sense": "limit of sums", "word": "integraali" }, { "_dis1": "34 34 8 9 15", "code": "fr", "lang": "French", "sense": "limit of sums", "tags": [ "feminine" ], "word": "intégrale" }, { "_dis1": "34 34 8 9 15", "code": "ka", "lang": "Georgian", "roman": "inṭegrali", "sense": "limit of sums", "word": "ინტეგრალი" }, { "_dis1": "34 34 8 9 15", "code": "de", "lang": "German", "sense": "limit of sums", "tags": [ "neuter" ], "word": "Integral" }, { "_dis1": "34 34 8 9 15", "code": "el", "lang": "Greek", "roman": "oloklíroma", "sense": "limit of sums", "tags": [ "neuter" ], "word": "ολοκλήρωμα" }, { "_dis1": "34 34 8 9 15", "code": "he", "lang": "Hebrew", "roman": "integrál", "sense": "limit of sums", "tags": [ "masculine" ], "word": "אִינְטֶגְרָל" }, { "_dis1": "34 34 8 9 15", "code": "he", "english": "Academy of the Hebrew Language", "lang": "Hebrew", "roman": "askémet", "sense": "limit of sums", "tags": [ "feminine" ], "word": "אַסְכֶּמֶת" }, { "_dis1": "34 34 8 9 15", "code": "hu", "lang": "Hungarian", "sense": "limit of sums", "word": "integrál" }, { "_dis1": "34 34 8 9 15", "code": "is", "lang": "Icelandic", "sense": "limit of sums", "tags": [ "feminine" ], "word": "heildun" }, { "_dis1": "34 34 8 9 15", "code": "is", "lang": "Icelandic", "sense": "limit of sums", "tags": [ "feminine" ], "word": "tegrun" }, { "_dis1": "34 34 8 9 15", "code": "it", "lang": "Italian", "sense": "limit of sums", "tags": [ "masculine" ], "word": "integrale" }, { "_dis1": "34 34 8 9 15", "alt": "せきぶん", "code": "ja", "lang": "Japanese", "roman": "sekibun", "sense": "limit of sums", "word": "積分" }, { "_dis1": "34 34 8 9 15", "code": "kk", "lang": "Kazakh", "roman": "integral", "sense": "limit of sums", "word": "интеграл" }, { "_dis1": "34 34 8 9 15", "code": "km", "lang": "Khmer", "roman": "ʼangteekraal", "sense": "limit of sums", "word": "អាំងតេក្រាល" }, { "_dis1": "34 34 8 9 15", "code": "ko", "lang": "Korean", "roman": "jeokbun", "sense": "limit of sums", "word": "적분" }, { "_dis1": "34 34 8 9 15", "code": "ky", "lang": "Kyrgyz", "roman": "integral", "sense": "limit of sums", "word": "интеграл" }, { "_dis1": "34 34 8 9 15", "code": "ms", "lang": "Malay", "sense": "limit of sums", "word": "kamiran" }, { "_dis1": "34 34 8 9 15", "code": "gv", "lang": "Manx", "sense": "limit of sums", "tags": [ "masculine" ], "word": "co-hym" }, { "_dis1": "34 34 8 9 15", "code": "mn", "lang": "Mongolian", "roman": "integral", "sense": "limit of sums", "word": "интеграл" }, { "_dis1": "34 34 8 9 15", "code": "no", "lang": "Norwegian", "sense": "limit of sums", "tags": [ "neuter" ], "word": "integral" }, { "_dis1": "34 34 8 9 15", "code": "pl", "lang": "Polish", "sense": "limit of sums", "tags": [ "feminine" ], "word": "całka" }, { "_dis1": "34 34 8 9 15", "code": "pl", "lang": "Polish", "sense": "limit of sums", "tags": [ "feminine" ], "word": "całka oznaczona" }, { "_dis1": "34 34 8 9 15", "code": "pt", "lang": "Portuguese", "sense": "limit of sums", "tags": [ "feminine" ], "word": "integral" }, { "_dis1": "34 34 8 9 15", "code": "ro", "lang": "Romanian", "sense": "limit of sums", "tags": [ "feminine" ], "word": "integrală" }, { "_dis1": "34 34 8 9 15", "code": "ru", "lang": "Russian", "roman": "intɛgrál", "sense": "limit of sums", "tags": [ "masculine" ], "word": "интегра́л" }, { "_dis1": "34 34 8 9 15", "code": "sh", "lang": "Serbo-Croatian", "sense": "limit of sums", "tags": [ "Cyrillic", "masculine" ], "word": "интѐгра̄л" }, { "_dis1": "34 34 8 9 15", "code": "sh", "lang": "Serbo-Croatian", "sense": "limit of sums", "tags": [ "Roman", "masculine" ], "word": "intègrāl" }, { "_dis1": "34 34 8 9 15", "code": "es", "lang": "Spanish", "sense": "limit of sums", "tags": [ "feminine" ], "word": "integral" }, { "_dis1": "34 34 8 9 15", "code": "su", "lang": "Sundanese", "sense": "limit of sums", "word": "integral" }, { "_dis1": "34 34 8 9 15", "code": "sv", "lang": "Swedish", "sense": "limit of sums", "tags": [ "common-gender" ], "word": "integral" }, { "_dis1": "34 34 8 9 15", "code": "tl", "lang": "Tagalog", "sense": "limit of sums", "word": "lagom" }, { "_dis1": "34 34 8 9 15", "code": "th", "lang": "Thai", "roman": "bpà-rí-pan", "sense": "limit of sums", "word": "ปริพันธ์" }, { "_dis1": "34 34 8 9 15", "code": "tr", "lang": "Turkish", "sense": "limit of sums", "word": "integral" }, { "_dis1": "34 34 8 9 15", "code": "uk", "lang": "Ukrainian", "roman": "intehrál", "sense": "limit of sums", "tags": [ "masculine" ], "word": "інтегра́л" }, { "_dis1": "34 34 8 9 15", "code": "vi", "lang": "Vietnamese", "sense": "limit of sums", "word": "tích phân" } ], "wikipedia": [ "integral" ], "word": "integral" }
{ "categories": [ "English adjectives", "English countable nouns", "English entries with incorrect language header", "English heteronyms", "English lemmas", "English nouns", "English terms borrowed from Middle French", "English terms derived from Latin", "English terms derived from Medieval Latin", "English terms derived from Middle French", "Entries with translation boxes", "Pages with 11 entries", "Pages with entries", "Requests for review of Hungarian translations", "Requests for review of Manx translations", "Terms with Arabic translations", "Terms with Armenian translations", "Terms with Bashkir translations", "Terms with Belarusian translations", "Terms with Bulgarian translations", "Terms with Cantonese translations", "Terms with Catalan translations", "Terms with Czech translations", "Terms with Dutch translations", "Terms with Esperanto translations", "Terms with Finnish translations", "Terms with French translations", "Terms with Georgian translations", "Terms with German translations", "Terms with Greek translations", "Terms with Hakka translations", "Terms with Hebrew translations", "Terms with Hungarian translations", "Terms with Icelandic translations", "Terms with Italian translations", "Terms with Japanese translations", "Terms with Kazakh translations", "Terms with Khmer translations", "Terms with Korean translations", "Terms with Kyrgyz translations", "Terms with Malay translations", "Terms with Mandarin translations", "Terms with Manx translations", "Terms with Mongolian translations", "Terms with Norwegian translations", "Terms with Polish translations", "Terms with Portuguese translations", "Terms with Romanian translations", "Terms with Russian translations", "Terms with Serbo-Croatian translations", "Terms with Spanish translations", "Terms with Sundanese translations", "Terms with Swedish translations", "Terms with Tagalog translations", "Terms with Thai translations", "Terms with Turkish translations", "Terms with Ukrainian translations", "Terms with Vietnamese translations", "en:Calculus", "en:Functions" ], "derived": [ { "word": "integral brick" }, { "word": "integral closure" }, { "word": "integral cosmology" }, { "word": "integral cuboid" }, { "word": "integral current" }, { "word": "integral curvature" }, { "word": "integral curve" }, { "word": "integral domain" }, { "word": "integral drawing" }, { "word": "integral ecology" }, { "word": "integral element" }, { "word": "integral energy" }, { "word": "integral extension" }, { "word": "integral fast reactor" }, { "word": "integral field unit" }, { "word": "integral function" }, { "word": "integral geometry" }, { "word": "integral graph" }, { "word": "integral homology group" }, { "word": "integral kernel" }, { "word": "integral membrane protein" }, { "word": "integral number" }, { "word": "integral politics" }, { "word": "integral polygedron" }, { "word": "integral polynomial" }, { "word": "integral post-metaphysics" }, { "word": "integral psychology" }, { "word": "integral transformative practice" }, { "word": "integral yoga" }, { "word": "integrity" }, { "word": "semi-integral" } ], "etymology_templates": [ { "args": { "1": "en", "2": "frm", "3": "integral" }, "expansion": "Borrowed from Middle French integral", "name": "bor+" }, { "args": { "1": "en", "2": "ML.", "3": "integrālis" }, "expansion": "Medieval Latin integrālis", "name": "der" }, { "args": { "1": "en", "2": "la", "3": "integer", "t": "entire" }, "expansion": "Latin integer (“entire”)", "name": "der" } ], "etymology_text": "Borrowed from Middle French integral, from Medieval Latin integrālis, from Latin integer (“entire”); see integer.", "forms": [ { "form": "more integral", "tags": [ "comparative" ] }, { "form": "most integral", "tags": [ "superlative" ] } ], "head_templates": [ { "args": {}, "expansion": "integral (comparative more integral, superlative most integral)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "related": [ { "word": "integer" }, { "word": "integrity" }, { "tags": [ "rare" ], "word": "integrous" } ], "senses": [ { "categories": [ "English terms with quotations" ], "examples": [ { "ref": "1692–1717, Robert South, Twelve Sermons Preached upon Several Occasions, volume (please specify |volume=I to VI), London:", "text": "Ceasing to do evil, and doing good, are the two great integral parts that complete this duty.", "type": "quote" } ], "glosses": [ "Constituting a whole together with other parts or factors; not omittable or removable" ], "links": [ [ "Constituting", "constitute" ], [ "whole", "whole" ], [ "part", "part" ], [ "factor", "factor" ], [ "omittable", "omittable" ], [ "removable", "removable" ] ], "synonyms": [ { "word": "immanent" }, { "word": "inherent" }, { "word": "necessary" }, { "word": "intrinsic" } ] }, { "categories": [ "en:Mathematics" ], "glosses": [ "Of, pertaining to, or being an integer." ], "links": [ [ "mathematics", "mathematics" ], [ "integer", "integer" ] ], "raw_glosses": [ "(mathematics) Of, pertaining to, or being an integer." ], "topics": [ "mathematics", "sciences" ] }, { "categories": [ "en:Mathematics" ], "glosses": [ "Relating to integration (“the process of finding the integral [noun] of a function”)." ], "links": [ [ "mathematics", "mathematics" ], [ "integration", "integration#English" ], [ "integral [noun", "integral#Noun" ], [ "function", "function" ] ], "raw_glosses": [ "(mathematics) Relating to integration (“the process of finding the integral [noun] of a function”)." ], "topics": [ "mathematics", "sciences" ] }, { "categories": [ "en:Algebra" ], "glosses": [ "Being the root of some monic polynomial in A." ], "links": [ [ "algebra", "algebra" ], [ "commutative algebra", "commutative algebra" ], [ "ring", "ring" ], [ "element", "element" ], [ "subring", "subring" ], [ "root", "root" ], [ "monic", "monic" ], [ "polynomial", "polynomial" ] ], "qualifier": "commutative algebra", "raw_glosses": [ "(algebra, commutative algebra, of a ring element in a ring B relative to a subring A) Being the root of some monic polynomial in A." ], "raw_tags": [ "of a ring element in a ring B relative to a subring A" ], "topics": [ "algebra", "mathematics", "sciences" ] }, { "categories": [ "English terms with obsolete senses", "English terms with quotations" ], "examples": [ { "ref": "1627 (indicated as 1626), Francis [Bacon], “(please specify the page, or |century=I to X)”, in Sylua Syluarum: Or A Naturall Historie. In Ten Centuries. […], London: […] William Rawley […]; [p]rinted by J[ohn] H[aviland] for William Lee […], →OCLC:", "text": "A local motion keepeth bodies integral.", "type": "quote" } ], "glosses": [ "Whole; undamaged." ], "links": [ [ "Whole", "whole" ], [ "undamaged", "undamaged" ] ], "raw_glosses": [ "(obsolete) Whole; undamaged." ], "tags": [ "obsolete" ] } ], "sounds": [ { "ipa": "/ˈɪntɪɡr(ə)l/", "tags": [ "UK" ] }, { "ipa": "/ɪnˈtɛɡr(ə)l/", "tags": [ "UK" ] }, { "enpr": "ĭn-tĕgʹrəl", "tags": [ "US" ] }, { "ipa": "/ˈɪntəɡɹəl/", "tags": [ "US" ] }, { "ipa": "/ɪnˈtɛɡɹəl/", "tags": [ "US" ] }, { "audio": "en-uk-integral-adjective.ogg", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/8/85/En-uk-integral-adjective.ogg/En-uk-integral-adjective.ogg.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/8/85/En-uk-integral-adjective.ogg" } ], "translations": [ { "code": "ba", "lang": "Bashkir", "roman": "ayırılğıhıź", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "айырылғыһыҙ" }, { "code": "bg", "lang": "Bulgarian", "roman": "nerazdelen", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "неразделен" }, { "code": "bg", "lang": "Bulgarian", "roman": "cjalosten", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "цялостен" }, { "code": "yue", "lang": "Chinese Cantonese", "roman": "jyun⁴ zing² ge³", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "完整嘅" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "wánzhěng de", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "完整的" }, { "code": "cs", "lang": "Czech", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "nedílný" }, { "code": "nl", "lang": "Dutch", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "integraal" }, { "code": "eo", "lang": "Esperanto", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "integra" }, { "code": "fi", "lang": "Finnish", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "olennainen" }, { "code": "fi", "lang": "Finnish", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "kokonaisuuteen kuuluva" }, { "code": "de", "lang": "German", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "integral" }, { "code": "de", "lang": "German", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "ein Ganzes ausmachend" }, { "code": "de", "english": "descriptive", "lang": "German", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "zur Erhaltung des Ganzen unentbehrlich" }, { "code": "el", "lang": "Greek", "roman": "anapóspastos", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "αναπόσπαστος" }, { "code": "he", "lang": "Hebrew", "roman": "integráli", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "אִינְטֶגְרָלִי" }, { "code": "kk", "lang": "Kazakh", "roman": "integraldy", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "интегралды" }, { "code": "kk", "lang": "Kazakh", "roman": "integraldyq", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "интегралдық" }, { "code": "km", "lang": "Khmer", "roman": "dael teang srong", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "ដែលទាំងស្រុង" }, { "code": "gv", "lang": "Manx", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "slane" }, { "code": "pl", "lang": "Polish", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "jednolity" }, { "code": "pl", "lang": "Polish", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "integralny" }, { "code": "pt", "lang": "Portuguese", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "integral" }, { "code": "ro", "lang": "Romanian", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "integral" }, { "code": "ru", "lang": "Russian", "roman": "neotʺjémlemyj", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "неотъе́млемый" }, { "code": "ru", "lang": "Russian", "roman": "nedelímyj", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "недели́мый" }, { "code": "ru", "lang": "Russian", "roman": "neotdelímyj", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "неотдели́мый" }, { "code": "sv", "lang": "Swedish", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "hel" }, { "code": "sv", "lang": "Swedish", "sense": "constituting a whole together with other parts or factors; not omittable or removable", "word": "enhetlig" }, { "code": "ar", "lang": "Arabic", "roman": "takāmul", "sense": "math: of, pertaining to, or being an integer", "tags": [ "masculine" ], "word": "تَكَامُل" }, { "code": "ba", "lang": "Bashkir", "roman": "bötön hanlı", "sense": "math: of, pertaining to, or being an integer", "word": "бөтөн һанлы" }, { "code": "cs", "lang": "Czech", "sense": "math: of, pertaining to, or being an integer", "word": "celočíselný" }, { "code": "nl", "lang": "Dutch", "sense": "math: of, pertaining to, or being an integer", "word": "geheel" }, { "code": "eo", "lang": "Esperanto", "sense": "math: of, pertaining to, or being an integer", "word": "entjera" }, { "code": "fi", "lang": "Finnish", "sense": "math: of, pertaining to, or being an integer", "word": "kokonaisluku-" }, { "code": "fr", "lang": "French", "sense": "math: of, pertaining to, or being an integer", "word": "intégral" }, { "code": "de", "lang": "German", "sense": "math: of, pertaining to, or being an integer", "word": "ganzzahlig" }, { "code": "el", "lang": "Greek", "roman": "akéraios", "sense": "math: of, pertaining to, or being an integer", "tags": [ "masculine" ], "word": "ακέραιος" }, { "code": "kk", "lang": "Kazakh", "roman": "integraldy", "sense": "math: of, pertaining to, or being an integer", "word": "интегралды" }, { "code": "kk", "lang": "Kazakh", "roman": "integraldyq", "sense": "math: of, pertaining to, or being an integer", "word": "интегралдық" }, { "code": "gv", "lang": "Manx", "sense": "math: of, pertaining to, or being an integer", "word": "slane-earrooagh" }, { "code": "pt", "lang": "Portuguese", "sense": "math: of, pertaining to, or being an integer", "word": "inteiro" }, { "code": "ro", "lang": "Romanian", "sense": "math: of, pertaining to, or being an integer", "word": "integral" }, { "code": "ru", "lang": "Russian", "roman": "celočíslennyj", "sense": "math: of, pertaining to, or being an integer", "word": "целочи́сленный" }, { "code": "es", "lang": "Spanish", "sense": "math: of, pertaining to, or being an integer", "word": "entero" }, { "code": "sv", "lang": "Swedish", "sense": "math: of, pertaining to, or being an integer", "word": "compounds with heltal" }, { "code": "tl", "lang": "Tagalog", "sense": "math: of, pertaining to, or being an integer", "word": "buumbilangin" }, { "code": "bg", "lang": "Bulgarian", "roman": "integralen", "sense": "math: relating to integration", "word": "интегрален" }, { "code": "eo", "lang": "Esperanto", "sense": "math: relating to integration", "word": "integrala" }, { "code": "fi", "lang": "Finnish", "sense": "math: relating to integration", "word": "integraali-" }, { "code": "fr", "lang": "French", "sense": "math: relating to integration", "word": "intégral" }, { "code": "kk", "lang": "Kazakh", "roman": "integraldy", "sense": "math: relating to integration", "word": "интегралды" }, { "code": "kk", "lang": "Kazakh", "roman": "integraldyq", "sense": "math: relating to integration", "word": "интегралдық" }, { "code": "es", "lang": "Spanish", "sense": "math: relating to integration", "word": "integral" } ], "word": "integral" } { "categories": [ "English adjectives", "English countable nouns", "English entries with incorrect language header", "English heteronyms", "English lemmas", "English nouns", "English terms borrowed from Middle French", "English terms derived from Latin", "English terms derived from Medieval Latin", "English terms derived from Middle French", "Entries with translation boxes", "Pages with 11 entries", "Pages with entries", "Requests for review of Hungarian translations", "Requests for review of Manx translations", "Terms with Arabic translations", "Terms with Armenian translations", "Terms with Bashkir translations", "Terms with Belarusian translations", "Terms with Bulgarian translations", "Terms with Cantonese translations", "Terms with Catalan translations", "Terms with Czech translations", "Terms with Dutch translations", "Terms with Esperanto translations", "Terms with Finnish translations", "Terms with French translations", "Terms with Georgian translations", "Terms with German translations", "Terms with Greek translations", "Terms with Hakka translations", "Terms with Hebrew translations", "Terms with Hungarian translations", "Terms with Icelandic translations", "Terms with Italian translations", "Terms with Japanese translations", "Terms with Kazakh translations", "Terms with Khmer translations", "Terms with Korean translations", "Terms with Kyrgyz translations", "Terms with Malay translations", "Terms with Mandarin translations", "Terms with Manx translations", "Terms with Mongolian translations", "Terms with Norwegian translations", "Terms with Polish translations", "Terms with Portuguese translations", "Terms with Romanian translations", "Terms with Russian translations", "Terms with Serbo-Croatian translations", "Terms with Spanish translations", "Terms with Sundanese translations", "Terms with Swedish translations", "Terms with Tagalog translations", "Terms with Thai translations", "Terms with Turkish translations", "Terms with Ukrainian translations", "Terms with Vietnamese translations", "en:Calculus", "en:Functions" ], "derived": [ { "word": "Barnes integral" }, { "word": "Choquet integral" }, { "word": "contour integral" }, { "word": "definite integral" }, { "word": "half-integral" }, { "word": "Hellinger integral" }, { "word": "improper integral" }, { "word": "indefinite integral" }, { "word": "integral calculus" }, { "word": "integral equation" }, { "word": "integral theory" }, { "word": "integral transform" }, { "word": "integration" }, { "word": "iterated integral" }, { "word": "Jackson integral" }, { "word": "Lebesgue integral" }, { "word": "line integral" }, { "word": "logarithmic integral" }, { "word": "Mellin-Barnes integral" }, { "word": "ordered integral domain" }, { "word": "particular integral" }, { "word": "path integral formalism" }, { "word": "Riemann integral" }, { "word": "Riemann-Stieltjes integral" }, { "word": "Sugeno integral" }, { "word": "surface integral" }, { "word": "Volterra integral equation" }, { "word": "volume integral" } ], "etymology_templates": [ { "args": { "1": "en", "2": "frm", "3": "integral" }, "expansion": "Borrowed from Middle French integral", "name": "bor+" }, { "args": { "1": "en", "2": "ML.", "3": "integrālis" }, "expansion": "Medieval Latin integrālis", "name": "der" }, { "args": { "1": "en", "2": "la", "3": "integer", "t": "entire" }, "expansion": "Latin integer (“entire”)", "name": "der" } ], "etymology_text": "Borrowed from Middle French integral, from Medieval Latin integrālis, from Latin integer (“entire”); see integer.", "forms": [ { "form": "integrals", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "integral (plural integrals)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "word": "integer" } ], "senses": [ { "categories": [ "English terms with usage examples", "en:Mathematics" ], "examples": [ { "text": "The integral of a univariate real-valued function is the area under its curve; but be warned! Not all functions are integrable!", "type": "example" } ], "glosses": [ "One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof." ], "links": [ [ "mathematics", "mathematics" ], [ "operations", "operations" ], [ "calculus", "calculus" ], [ "differentiation", "differentiation" ], [ "function", "function" ], [ "displacement", "displacement" ], [ "area", "area" ], [ "volume", "volume" ], [ "infinitesimal", "infinitesimal" ], [ "limiting", "limit" ], [ "sequence", "sequence" ], [ "partial sum", "partial sum" ], [ "long s", "long s" ], [ "∫", "∫" ] ], "raw_glosses": [ "(mathematics) One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof." ], "topics": [ "mathematics", "sciences" ] }, { "categories": [ "English terms with usage examples", "en:Mathematics" ], "glosses": [ "One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof.", "Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc." ], "links": [ [ "mathematics", "mathematics" ], [ "operations", "operations" ], [ "calculus", "calculus" ], [ "differentiation", "differentiation" ], [ "function", "function" ], [ "displacement", "displacement" ], [ "area", "area" ], [ "volume", "volume" ], [ "infinitesimal", "infinitesimal" ], [ "limiting", "limit" ], [ "sequence", "sequence" ], [ "partial sum", "partial sum" ], [ "long s", "long s" ], [ "∫", "∫" ], [ "analytic", "analysis" ], [ "formalization", "formalization" ], [ "Riemann integral", "Riemann integral" ], [ "Lebesgue integral", "Lebesgue integral" ] ], "raw_glosses": [ "(mathematics) One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof.", "(specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc." ], "tags": [ "specifically" ], "topics": [ "mathematics", "sciences" ] }, { "categories": [ "English terms with usage examples", "en:Mathematics" ], "examples": [ { "text": "The integral of #x5C;frac#x7B;1#x7D;#x7B;x#x7D; on #x5B;#x5C;frac#x7B;1#x7D;#x7B;2#x7D;,1#x5D; is #x5C;ln(2), but the integral of the same function on (0,1#x5D; diverges. In notation, #x5C;int#x5F;#x5C;frac#x7B;1#x7D;#x7B;2#x7D;¹#x5C;frac#x7B;1#x7D;#x7B;x#x7D;dx#x3D;#x5C;ln(2), but #x5C;int#x5F;0¹#x5C;frac#x7B;1#x7D;#x7B;x#x7D;dx#x3D;#x5C;infty.", "type": "example" }, { "text": "Stokes' theorem relates the integral over a surface of the curl of a vector field to a line integral around the boundary of that surface: #x5C;int#x5F;S#x5C;nabla#x5C;times#x5C;mathbf#x7B;F#x7D;#x5C;cdotd#x5C;mathbf#x7B;S#x7D;#x3D;#x5C;int#x5F;#x7B;#x5C;partialS#x7D;#x5C;mathbf#x7B;F#x7D;#x5C;cdotd#x5C;mathbf#x7B;r#x7D;,.", "type": "example" } ], "glosses": [ "A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of the integrand (or, generally, differential form) appearing in front of the integral sign." ], "links": [ [ "mathematics", "mathematics" ], [ "definite integral", "definite integral" ], [ "application", "application" ], [ "subset", "subset" ], [ "domain", "domain" ], [ "number", "number" ], [ "positive", "positive" ], [ "negative", "negative" ], [ "infinity", "infinity" ], [ "finite", "finite" ], [ "converge", "converge" ], [ "diverge", "diverge" ], [ "interval", "interval" ], [ "integrand", "integrand" ], [ "differential form", "differential form" ] ], "raw_glosses": [ "(mathematics) A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of the integrand (or, generally, differential form) appearing in front of the integral sign." ], "topics": [ "mathematics", "sciences" ] }, { "antonyms": [ { "word": "derivative" } ], "categories": [ "English terms with usage examples", "en:Mathematics" ], "examples": [ { "text": "The integral of x² is #x5C;frac#x7B;x³#x7D;#x7B;3#x7D; plus a constant.", "type": "example" } ], "glosses": [ "An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;" ], "links": [ [ "mathematics", "mathematics" ], [ "indefinite integral", "indefinite integral" ], [ "indefinite", "indefinite" ], [ "antiderivative", "antiderivative" ] ], "raw_glosses": [ "(mathematics) An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;" ], "synonyms": [ { "word": "antiderivative" }, { "word": "indefinite integral" }, { "word": "∫" } ], "topics": [ "mathematics", "sciences" ] }, { "antonyms": [ { "word": "derivative" } ], "categories": [ "English terms with usage examples", "en:Mathematics" ], "glosses": [ "An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;", "The fluent of a given fluxion in Newtonian calculus." ], "links": [ [ "mathematics", "mathematics" ], [ "indefinite integral", "indefinite integral" ], [ "indefinite", "indefinite" ], [ "antiderivative", "antiderivative" ], [ "fluent", "fluent" ], [ "fluxion", "fluxion" ], [ "Newtonian", "Newtonian" ] ], "raw_glosses": [ "(mathematics) An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;", "(mathematics, historical or obsolete) The fluent of a given fluxion in Newtonian calculus." ], "synonyms": [ { "word": "antiderivative" }, { "word": "indefinite integral" }, { "word": "∫" } ], "tags": [ "historical", "obsolete" ], "topics": [ "mathematics", "sciences" ] } ], "sounds": [ { "enpr": "ĭnʹtĭ-grəl", "tags": [ "UK" ] }, { "ipa": "/ˈɪntɪɡɹ(ə)l/", "tags": [ "UK" ] }, { "enpr": "ĭnʹtə-grəl", "tags": [ "US" ] }, { "ipa": "/ˈɪntəɡɹəl/", "tags": [ "US" ] }, { "ipa": "/ɪnˈtɛɡɹəl/", "tags": [ "US" ] }, { "audio": "en-uk-integral-noun.ogg", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/b/bc/En-uk-integral-noun.ogg/En-uk-integral-noun.ogg.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/b/bc/En-uk-integral-noun.ogg" } ], "translations": [ { "code": "hy", "lang": "Armenian", "roman": "integral", "sense": "limit of sums", "word": "ինտեգրալ" }, { "code": "be", "lang": "Belarusian", "roman": "intehrál", "sense": "limit of sums", "tags": [ "masculine" ], "word": "інтэгра́л" }, { "code": "bg", "lang": "Bulgarian", "roman": "integrál", "sense": "limit of sums", "tags": [ "masculine" ], "word": "интегра́л" }, { "code": "ca", "lang": "Catalan", "sense": "limit of sums", "tags": [ "feminine" ], "word": "integració" }, { "code": "yue", "lang": "Chinese Cantonese", "sense": "limit of sums", "word": "積分" }, { "code": "yue", "lang": "Chinese Cantonese", "roman": "zik¹ fan¹", "sense": "limit of sums", "word": "积分" }, { "code": "hak", "lang": "Hakka Chinese", "sense": "limit of sums", "word": "chit-fûn-ho̍k" }, { "code": "cmn", "lang": "Chinese Mandarin", "sense": "limit of sums", "word": "積分" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "jī fēn", "sense": "limit of sums", "word": "积分" }, { "code": "cs", "lang": "Czech", "sense": "limit of sums", "tags": [ "masculine" ], "word": "integrál" }, { "code": "nl", "lang": "Dutch", "sense": "limit of sums", "word": "integraal" }, { "code": "eo", "lang": "Esperanto", "sense": "limit of sums", "word": "integralo" }, { "code": "eo", "lang": "Esperanto", "sense": "limit of sums", "word": "integro" }, { "code": "fi", "lang": "Finnish", "sense": "limit of sums", "word": "integraali" }, { "code": "fr", "lang": "French", "sense": "limit of sums", "tags": [ "feminine" ], "word": "intégrale" }, { "code": "ka", "lang": "Georgian", "roman": "inṭegrali", "sense": "limit of sums", "word": "ინტეგრალი" }, { "code": "de", "lang": "German", "sense": "limit of sums", "tags": [ "neuter" ], "word": "Integral" }, { "code": "el", "lang": "Greek", "roman": "oloklíroma", "sense": "limit of sums", "tags": [ "neuter" ], "word": "ολοκλήρωμα" }, { "code": "he", "lang": "Hebrew", "roman": "integrál", "sense": "limit of sums", "tags": [ "masculine" ], "word": "אִינְטֶגְרָל" }, { "code": "he", "english": "Academy of the Hebrew Language", "lang": "Hebrew", "roman": "askémet", "sense": "limit of sums", "tags": [ "feminine" ], "word": "אַסְכֶּמֶת" }, { "code": "hu", "lang": "Hungarian", "sense": "limit of sums", "word": "integrál" }, { "code": "is", "lang": "Icelandic", "sense": "limit of sums", "tags": [ "feminine" ], "word": "heildun" }, { "code": "is", "lang": "Icelandic", "sense": "limit of sums", "tags": [ "feminine" ], "word": "tegrun" }, { "code": "it", "lang": "Italian", "sense": "limit of sums", "tags": [ "masculine" ], "word": "integrale" }, { "alt": "せきぶん", "code": "ja", "lang": "Japanese", "roman": "sekibun", "sense": "limit of sums", "word": "積分" }, { "code": "kk", "lang": "Kazakh", "roman": "integral", "sense": "limit of sums", "word": "интеграл" }, { "code": "km", "lang": "Khmer", "roman": "ʼangteekraal", "sense": "limit of sums", "word": "អាំងតេក្រាល" }, { "code": "ko", "lang": "Korean", "roman": "jeokbun", "sense": "limit of sums", "word": "적분" }, { "code": "ky", "lang": "Kyrgyz", "roman": "integral", "sense": "limit of sums", "word": "интеграл" }, { "code": "ms", "lang": "Malay", "sense": "limit of sums", "word": "kamiran" }, { "code": "gv", "lang": "Manx", "sense": "limit of sums", "tags": [ "masculine" ], "word": "co-hym" }, { "code": "mn", "lang": "Mongolian", "roman": "integral", "sense": "limit of sums", "word": "интеграл" }, { "code": "no", "lang": "Norwegian", "sense": "limit of sums", "tags": [ "neuter" ], "word": "integral" }, { "code": "pl", "lang": "Polish", "sense": "limit of sums", "tags": [ "feminine" ], "word": "całka" }, { "code": "pl", "lang": "Polish", "sense": "limit of sums", "tags": [ "feminine" ], "word": "całka oznaczona" }, { "code": "pt", "lang": "Portuguese", "sense": "limit of sums", "tags": [ "feminine" ], "word": "integral" }, { "code": "ro", "lang": "Romanian", "sense": "limit of sums", "tags": [ "feminine" ], "word": "integrală" }, { "code": "ru", "lang": "Russian", "roman": "intɛgrál", "sense": "limit of sums", "tags": [ "masculine" ], "word": "интегра́л" }, { "code": "sh", "lang": "Serbo-Croatian", "sense": "limit of sums", "tags": [ "Cyrillic", "masculine" ], "word": "интѐгра̄л" }, { "code": "sh", "lang": "Serbo-Croatian", "sense": "limit of sums", "tags": [ "Roman", "masculine" ], "word": "intègrāl" }, { "code": "es", "lang": "Spanish", "sense": "limit of sums", "tags": [ "feminine" ], "word": "integral" }, { "code": "su", "lang": "Sundanese", "sense": "limit of sums", "word": "integral" }, { "code": "sv", "lang": "Swedish", "sense": "limit of sums", "tags": [ "common-gender" ], "word": "integral" }, { "code": "tl", "lang": "Tagalog", "sense": "limit of sums", "word": "lagom" }, { "code": "th", "lang": "Thai", "roman": "bpà-rí-pan", "sense": "limit of sums", "word": "ปริพันธ์" }, { "code": "tr", "lang": "Turkish", "sense": "limit of sums", "word": "integral" }, { "code": "uk", "lang": "Ukrainian", "roman": "intehrál", "sense": "limit of sums", "tags": [ "masculine" ], "word": "інтегра́л" }, { "code": "vi", "lang": "Vietnamese", "sense": "limit of sums", "word": "tích phân" } ], "wikipedia": [ "integral" ], "word": "integral" }
Download raw JSONL data for integral meaning in English (31.4kB)
{ "called_from": "translations/324", "msg": "possible sense number in translation item: Hungarian: __IGNORE__ (2)", "path": [ "integral" ], "section": "English", "subsection": "adjective", "title": "integral", "trace": "" }
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