# Stokes' Theorem

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Stoke's Theorem is a generalization of the Fundamental Theorem of Calculus, which states that if *M* is an oriented piece-wise smooth manifold of dimension k and is a smooth (*k*−1)-form with compact support on *M*. Let ∂*M* denotes the boundary of *M* with its induced orientation, then

- ,

where *d* is the exterior derivative.