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

Step by Step Answer:

To apply Greens Theorem to the line integral ointC y2 dx x2 dy we first need to identify F1 and F2 from the line integral which are the components of ...View the full answer

Calculus

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