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Khan, S.A. and Sanderson, G. (2011) Fundamental Theorem of Line Integrals (Article). Khan Academy.
https://www.khanacademy.org/math/multivariable-calculus/integrating-multivariable-functions/line-integrals-in-vector-fields-articles/a/fundamental-theorem-of-line-integrals

has been cited by the following article:

• TITLE: Conservative Vector Fields and the Intersect Rule

  AUTHORS: Daniel A. Jaffa

  KEYWORDS: Vector Physics, Vector Calculus, Multivariable Calculus, Gradient Fields, Vector Fields, Conservative Vector Fields, Newtonian Mechanics

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.10, October 20, 2023

  ABSTRACT: This paper covers the concept of a conservative vector field, and its application in vector physics and Newtonian mechanics. Conservative vector fields are defined as the gradient of a scalar-valued potential function. Gradient fields are irrotational, as in the curl in all conservative vector fields is zero, by Clairaut’s Theorem. Additionally, line integrals in conservative vector fields are path-independent, and line integrals over closed paths are always equal to zero, properties proved by the Gradient Theorem of multivariable calculus. Gradient fields represent conservative forces, and the associated potential function is analogous to potential energy associated with said conservative forces. The Intersect Rule provides a new, unique shortcut for determining if a vector field is conservative and deriving potential functions, by treating the indefinite integral as a set of infinitely many functions which satisfy the integral.