📚 name • entry_id 63265
fundamental theorem of calculus for line integrals
Meanings (ES + gloss)
teorema fundamental de las integrales de línea • teorema fundamental para integrales de línea
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)).
Phrases
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