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 921: 50



Work Step by Step

$ V=\int^{\pi/6}_0 \int^{\pi/2}_0 \int^a_0 p^2 \sin\phi $ $ dp $ $ d\phi d\theta $ =$\frac{a^3}{3}\int^{\pi/6}_0 \int^{\pi/2}_0 \sin\phi d\phi d\theta $ =$\frac{a^3}{3}\int^{\pi/6}_0 d\theta $ =$\frac{a^3\pi}{18}$
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