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: 13



Work Step by Step

Applying Stoke's Theorem, we have $\oint F \cdot dr=\iint _S (\nabla \times F) \cdot n d\sigma$ $r_u=\lt \cos v,\sin v,-2u \gt$ and $r_u=\lt -u\sin v,u\cos v,0 \gt$ Then, we have $\iint _S (\nabla \times F) \cdot n d\sigma=\int _{0}^{2 \pi}\int_{0}^{2} (10 u^2 \cos v+4u^2 \sin v+3u) du dv $ This implies that $\int _{0}^{2 \pi} [ \dfrac{80}{3}\cos v+\dfrac{32}{3}\sin v+6]dv=12\pi$
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