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: 38

Answer

$\frac{8\pi}{3}$

Work Step by Step

V=$\int^{2\pi}_0 \int^{\pi/2}_{\pi/3} \int^2_0 p^2sin\phi dp d\phi d\theta $ =$\frac{8}{3}\int^{2\pi}_0 \int^{\pi/2}_{\pi/3} \sin \phi d\phi $ $ d\theta $ =$\frac{8}{3}\int^{2\pi}_0 [-cos\phi]^{\pi/2}_{\pi/3} d\theta $ =$\frac{4}{3}\int^{2\pi}_0 d\theta $ =$\frac{8\pi}{3}$
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