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 919: 14

Answer

$\frac{2}{5}$

Work Step by Step

$\int^{\pi/2}_{-\pi/2} \int^1_0 \int^{r \cos \theta}_0 r^3 dz dr d\theta$ =$\int^{\pi/2}_{-\pi/2} \int^1_0 r^4 cos\theta dr d\theta $ =$\frac{1}{5}\int^{\pi/2}_{-\pi/2}cos\theta $ =$\frac{2}{5}$
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