fundamental theorem of calculus for line integrals

proper noun

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

“∫_C∇f·d mathbf r=f( mathbf r(b))-f( mathbf r(a)).”

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Meanings

proper nounthe fundamental theorem of calculus for line integrals
  1. calculusA 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

    ∫_C∇f·d mathbf r=f( mathbf r(b))-f( mathbf r(a)).

Translations

Bulgarian фундаментална теорема на криволинейните интеграли
  • фундаментална теорема на криволинейните интеграли (fundamentalna teorema na krivolinejnite integrali)theorem
French théorème fondamental des intégrales curvilignes
  • théorème fondamental des intégrales curvilignestheorem
Portuguese teorema fundamental para as integrais de linha
  • teorema fundamental para as integrais de linhatheorem
Spanish teorema fundamental para integrales de línea, teorema fundamental de las integrales de línea
  • teorema fundamental para integrales de líneatheorem
  • teorema fundamental de las integrales de líneatheorem
Cite this entry
APA

fundamental theorem of calculus for line integrals. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/fundamental%20theorem%20of%20calculus%20for%20line%20integrals

MLA

“fundamental theorem of calculus for line integrals.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/fundamental%20theorem%20of%20calculus%20for%20line%20integrals. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “fundamental theorem of calculus for line integrals,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/fundamental%20theorem%20of%20calculus%20for%20line%20integrals.

Source: fundamental theorem of calculus for line integrals on Wiktionary, CC BY-SA 4.0.