Compute the flux (oint_{partial mathcal{D}} mathbf{F} cdot mathbf{n} d s) of (mathbf{F}(x, y)=leftlangle x^{3}+2 x, y^{3}+yightangle) across

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Compute the flux $\oint_{\partial \mathcal{D}} \mathbf{F} \cdot \mathbf{n} d s$ of $\mathbf{F}(x, y)=\left\langle x^{3}+2 x, y^{3}+yightangle$ across the circle $\mathcal{D}$ given by $x^{2}+y^{2}=4$ using the vector form of 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 12:03 AM

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Compute the flux (oint_{partial mathcal{D}} mathbf{F} cdot mathbf{n} d s) of (mathbf{F}(x, y)=leftlangle x^{3}+2 x, y^{3}+yightangle) across

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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 |$ Fidx + F2dy = SS (/ (357 aD a Fi dA

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Calculus

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