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

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

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$\oint_{C} y e^{x} d x+x e^{y} d y$, where $C$ is the triangle with vertices $(-1,0),(0,4)$, and $(0,1)$, oriented counterclockwise

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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 e^{x} 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 Fi f Fdx + Fdy = = 16 (f/ TL (SF2-F1) a dA D

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To evaluate the line integral around the given closed curve using Greens Theorem we first need to identify the vector field whose line integral we are ...View the full answer

Calculus

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