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Definition: Let C be a positively orientated, piecewise-smooth, simple closed curve in the plane and let D be the region bounded by C. If P and Q have continuous partial derivatives on an open region that contains D, then int_C Pdx + Qdy = int int_D (dQ/dx - dP/dy)dA.
Source: Multivariable Calculus, 7th edition by James Stewart