where is the gradient, and the integral is a line integral. It is this relationship which makes the definition of a scalar potential function so useful in gravitation and electromagnetism as a concise way to encode information about a vector field.
See alsoDivergence Theorem, Green's Theorem, Line Integral, Poincaré's Theorem
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Cite this as:
Weisstein, Eric W. "Gradient Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GradientTheorem.html