Let C be the boundary of a region on which Green’s Theorem holds. Use Green’s Theorem to calculate

If a simple closed curve C in the plane and the region R it encloses satisfy the hypotheses of Green’s Theorem, the area of R is given by

The reason is that by Equation (4), run backward,

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a. b. $ s C f(x) dx + g(y) dy ky dx + hx dy (k and h constants).