"fundamental theorem of calculus for line integrals" meaning in All languages combined

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        {
          "text": "∫_C∇f·d mathbf r=f( mathbf r(b))-f( mathbf r(a))."
        }
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        "A generalization of the fundamental theorem of calculus to line integrals of vector fields, which states that the line integral of a conservative vector field along a path can be computed by evaluating the potential function at the endpoints of the path. Specifically, given a potential function f with continuous first partial derivatives on an open region R containing a curve C parameterized by mathbf r(t) for a≤t≤b"
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        "(calculus) A generalization of the fundamental theorem of calculus to line integrals of vector fields, which states that the line integral of a conservative vector field along a path can be computed by evaluating the potential function at the endpoints of the path. Specifically, given a potential function f with continuous first partial derivatives on an open region R containing a curve C parameterized by mathbf r(t) for a≤t≤b:"
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          "code": "bg",
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          "roman": "fundamentalna teorema na krivolinejnite integrali",
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          "word": "théorème fondamental des intégrales curvilignes"
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          "word": "teorema fundamental para as integrais de linha"
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          "word": "teorema fundamental para integrales de línea"
        },
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            "masculine"
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          "word": "teorema fundamental de las integrales de línea"
        }
      ]
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  "word": "fundamental theorem of calculus for line integrals"
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        "A generalization of the fundamental theorem of calculus to line integrals of vector fields, which states that the line integral of a conservative vector field along a path can be computed by evaluating the potential function at the endpoints of the path. Specifically, given a potential function f with continuous first partial derivatives on an open region R containing a curve C parameterized by mathbf r(t) for a≤t≤b"
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        "(calculus) A generalization of the fundamental theorem of calculus to line integrals of vector fields, which states that the line integral of a conservative vector field along a path can be computed by evaluating the potential function at the endpoints of the path. Specifically, given a potential function f with continuous first partial derivatives on an open region R containing a curve C parameterized by mathbf r(t) for a≤t≤b:"
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      "code": "bg",
      "lang": "Bulgarian",
      "roman": "fundamentalna teorema na krivolinejnite integrali",
      "sense": "theorem",
      "tags": [
        "feminine"
      ],
      "word": "фундаментална теорема на криволинейните интеграли"
    },
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      "sense": "theorem",
      "tags": [
        "masculine"
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      "word": "théorème fondamental des intégrales curvilignes"
    },
    {
      "code": "pt",
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      "sense": "theorem",
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        "masculine"
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      "word": "teorema fundamental para as integrais de linha"
    },
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      "sense": "theorem",
      "tags": [
        "masculine"
      ],
      "word": "teorema fundamental para integrales de línea"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "theorem",
      "tags": [
        "masculine"
      ],
      "word": "teorema fundamental de las integrales de línea"
    }
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  "word": "fundamental theorem of calculus for line integrals"
}