Use Green's Theorem to evaluate the line integral around the given closed curve. (oint_{C} y^{2} d x-x^{2}

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

image text in transcribed $\oint_{C} y^{2} d x-x^{2} d y$, where $C$ consists of the arcs $y=x^{2}$ and $y=\sqrt{x}, 0 \leq x \leq 1$, oriented clockwise

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Jan 28, 2024 12:03 AM

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Use Green's Theorem to evaluate the line integral around the given closed curve. (oint_{C} y^{2} d x-x^{2}

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 Fi f F dx + Fdy = - 16 (f/ 16 (352-351) a dA D

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Calculus

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