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In vector calculus and differential geometry, the generalized Stokes' theorem or just Stokes' theorem relates the integral of a function over the boundary of a manifold to the integral of the function's exterior derivative on the manifold itself. Mathematically, it is stated as

$\int_{\partial \Omega} \omega = \int_{\Omega} d \omega$

The fundamental theorem of calculus, gradient theorem, Green's theorem, divergence theorem, and Kelvin–Stokes theorem are all special cases of Stokes' theorem.