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In some sense, this says that integration is the opposite of differentiation.
The fundamental theorem of line integrals, also known as the gradient theorem, is one of several ways to extend this theorem into higher dimensions. In a sense, it says that line integration through a vector field is the opposite of the gradient. The statement of the theorem is that
Where
fstart color blueE, f, end color blueE is some scalar-valued multivariable function.
∇fdel, start color blueE, f, end color blueE is the gradient of fstart color blueE, f, end color blueE.