Using Green’s TheoremCalculating Area with Green’s Theorem

Chapter 16, Problem 25E

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Problem 25E

Using Green’s Theorem

Calculating Area with Green’s Theorem 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 (3), run backward,

Use the Green’s Theorem area formula given above to find the areas of the regions enclosed by the curves in Exercise

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