Stokes' Theorem

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Stoke's Theorem is the fundamental theorem of Exterior Calculus and 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.