Let (mathbf{F}(x, y)=leftlangle x+y^{2}, x^{2}-yightangle), and let (C) be the unit circle, oriented counterclockwise. Evaluate (oint_{C} mathbf{F}

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Let $\mathbf{F}(x, y)=\left\langle x+y^{2}, x^{2}-yightangle$, and let $C$ be the unit circle, oriented counterclockwise. Evaluate $\oint_{C} \mathbf{F} \cdot d \mathbf{r}$ directly as a line integral and using Green's Theorem.

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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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Let (mathbf{F}(x, y)=leftlangle x+y^{2}, x^{2}-yightangle), and let (C) be the unit circle, oriented counterclockwise. Evaluate (oint_{C} mathbf{F}

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THEOREM 1 Green's Theorem Let D be a domain whose boundary 3D is a simple closed curve, oriented counterclockwise. If F and F2 have continuous partial deriva- tives in an open region containing D, then & Fdx + F2 dy = = 16 ( 3F/ d aFi x ay dA aD 2

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Calculus

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