University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 15 - Section 15.7 - Stokes' Theorem - Exercises - Page 896: 9


$2 \pi a^2$

Work Step by Step

Applying Stoke's Theorem, we have $\oint F \cdot dr=\iint _S (\nabla \times F) \cdot n d\sigma$ Here, $F \cdot \dfrac{dr}{dt}=ay \sin t+ax \cos t=a^2 \sin^2 t+a^2 \cos^2 t=a^2$ Then, we have Flux of $(\nabla \times F)$=$\iint _S (\nabla \times F) \cdot n d\sigma=\int _{0}^{2\pi} a^2 dt$ This implies that $\int _{0}^{2\pi} a^2 dt=2 \pi a^2$
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