Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwse indicated. (oint_{C} y^{2}

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Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwse indicated.

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$\oint_{C} y^{2} d x+x^{2} d y$, where $C$ is the boundary of the square that is given by $0 \leq x \leq 1,0 \leq y \leq 1$

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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 12:00 AM

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Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwse indicated. $\oint_{C} y^{2} d x+x^{2} d y$, where $C$ is the boundary of the square \(-1 \leq...
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Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwse indicated. (oint_{C} y^{2}

Question:

THEOREM 1 Green's Theorem Let D be a domain whose boundary D is a simple closed curve, oriented counterclockwise. If F and F have continuous partial deriva- tives in an open region containing D, then $o F1 dx + F2 dy 1 (F2-F) da dA = ay 2

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We have Py2 and Qx2 therefore fracpartial Qpartial xfracpartial Ppart...View the full answer

Calculus

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