Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 15 - Multiple Integrals - Review - Exercises - Page 1102: 27



Work Step by Step

$\int\int_{D}(x^{2}+y^{2})^{3/2}dA=\int_{0}^{\pi/3}\int_{0} ^{3} r^{3}rdrd\theta$ $=\int_{0}^{\pi/3}\frac{ r^{5}}{5}|_{0}^{3}d\theta$ $=\int_{0}^{\pi/3}\frac{ 3^{5}}{5}|d\theta$ $=\int_{0}^{\pi/3}\frac{ 243}{5}|d\theta$ $=[\frac{ 243}{5}\theta]|_{0}^{\pi/3}$ $=\frac{ 243}{5}(\pi/3-0)$ $=\frac{81\pi}{5}$
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