Use Greens Theorem to prove the change of variables formula for a double integral

Chapter 16, Problem 31

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Use Greens Theorem to prove the change of variables formula for a double integral (Formula 15.10.9) for the case where f _x, y_ _ 1: Here is the region in the -plane that corresponds to the region in the -plane under the transformation given by , . [Hint: Note that the left side is and apply the first part of Equation 5. Convert the line integral over to a line integral over and apply Greens Theorem in the -plane.]

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