"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": [
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        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
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        },
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          "name": "Terms with Russian translations",
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
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        }
      ],
      "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": "fr",
          "lang": "French",
          "sense": "a type of integral",
          "tags": [
            "feminine"
          ],
          "word": "intégrale de Riemann"
        },
        {
          "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": [
    {
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      "expansion": "Riemann integral (plural Riemann integrals)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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        "Terms with French translations",
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        "Terms with Russian translations",
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      ],
      "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": "fr",
      "lang": "French",
      "sense": "a type of integral",
      "tags": [
        "feminine"
      ],
      "word": "intégrale de Riemann"
    },
    {
      "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"
}