Use Green's Theorem to evaluate the line integral around the given closed curve. (oint_{C} x y^{3} d

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Use Green's Theorem to evaluate the line integral around the given closed curve.

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$\oint_{C} x y^{3} d x+x^{3} y d y$, where $C$ is the boundary of the rectangle $-1 \leq x \leq 2,-2 \leq y \leq 3$, oriented counterclockwise

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Use Green's Theorem to evaluate the line integral around the given closed curve. (oint_{C} x y^{3} d

Question:

THEOREM 1 Green's Theorem Let D be a domain whose boundary 3D is a simple closed curve, oriented counterclockwise. If F and F have continuous partial deriva- tives in an open region containing D, then aF $ Fdx + Fdy = 1/ (23/7- D x a Fi y d dA

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Calculus

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