Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 15: Multiple Integrals - Section 15.7 - Triple Integrals in Cylindrical and Spherical Coordinates - Exercises 15.7 - Page 920: 45

Answer

$\frac{9}{4}$

Work Step by Step

$ V=\int^{2\pi}_{3\pi/2} \int^{3cos\theta}_0 \int^{-rsin\theta}_0 dz $ r dr $ d\theta $ =$\int^{2\pi}_{3\pi/2} \int^{3cos\theta}_0(-r^2\sin\theta) dr d\theta $ =$\int^{2\pi}_{3\pi/2} (-9cos^3\theta)(sin\theta)$ d\theta =$[\frac{9}{4}cos^4\theta]^{2\pi}_{3\pi/2}$ =$\frac{9}{4}-0$ =$\frac{9}{4}$
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