"Riemann integral" meaning in English

{
  "etymology_text": "Named after Bernhard Riemann, a German mathematician.",
  "forms": [
    {
      "form": "Riemann integrals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Riemann integral (plural Riemann integrals)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A type of integral whose computation involves dividing the interval of integration into smaller sub-intervals, summing sample values of the integrand inside those sub-intervals multiplied by their lengths, and letting the number of sub-intervals tend to infinity."
      ],
      "id": "en-Riemann_integral-en-noun-sHBfAjgn",
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "integral",
          "integral#English"
        ],
        [
          "interval",
          "interval#English"
        ],
        [
          "integrand",
          "integrand#English"
        ],
        [
          "infinity",
          "infinity#English"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) A type of integral whose computation involves dividing the interval of integration into smaller sub-intervals, summing sample values of the integrand inside those sub-intervals multiplied by their lengths, and letting the number of sub-intervals tend to infinity."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "a type of integral",
          "tags": [
            "neuter"
          ],
          "word": "Riemann-Integral"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "a type of integral",
          "tags": [
            "neuter"
          ],
          "word": "Riemannintegral"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "a type of integral",
          "tags": [
            "neuter"
          ],
          "word": "riemannsches Integral"
        },
        {
          "code": "ru",
          "lang": "Russian",
          "roman": "integrál Rímana",
          "sense": "a type of integral",
          "tags": [
            "masculine"
          ],
          "word": "интегра́л Ри́мана"
        }
      ],
      "wikipedia": [
        "Riemann integral"
      ]
    }
  ],
  "word": "Riemann integral"
}

{
  "etymology_text": "Named after Bernhard Riemann, a German mathematician.",
  "forms": [
    {
      "form": "Riemann integrals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Riemann integral (plural Riemann integrals)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English entries with language name categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with non-redundant non-automated sortkeys",
        "en:Mathematical analysis"
      ],
      "glosses": [
        "A type of integral whose computation involves dividing the interval of integration into smaller sub-intervals, summing sample values of the integrand inside those sub-intervals multiplied by their lengths, and letting the number of sub-intervals tend to infinity."
      ],
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "integral",
          "integral#English"
        ],
        [
          "interval",
          "interval#English"
        ],
        [
          "integrand",
          "integrand#English"
        ],
        [
          "infinity",
          "infinity#English"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) A type of integral whose computation involves dividing the interval of integration into smaller sub-intervals, summing sample values of the integrand inside those sub-intervals multiplied by their lengths, and letting the number of sub-intervals tend to infinity."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Riemann integral"
      ]
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "a type of integral",
      "tags": [
        "neuter"
      ],
      "word": "Riemann-Integral"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "a type of integral",
      "tags": [
        "neuter"
      ],
      "word": "Riemannintegral"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "a type of integral",
      "tags": [
        "neuter"
      ],
      "word": "riemannsches Integral"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "integrál Rímana",
      "sense": "a type of integral",
      "tags": [
        "masculine"
      ],
      "word": "интегра́л Ри́мана"
    }
  ],
  "word": "Riemann integral"
}