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: 46

Answer

12

Work Step by Step

$ V=2\int^{\pi}_{\pi/2} \int^{-3cos\theta}_0 \int^r_0$ dz r dr $ d\theta $ =$2\int^{\pi}_{\pi/2} \int^{-3cos\theta}_0 r^2 dr $ d $\theta $ =$\frac{2}{3}\int^{\pi}_{\pi/2} (-27cos^3\theta) d\theta $ =$-18([\frac{cos^2\theta\sin\theta}{3}]^\pi_{\pi/2}+\frac{2}{3}\int^\pi_{\pi/2}cos\theta d\theta)$ =12
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