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: 25

Answer

$5\pi $

Work Step by Step

$\int^{2\pi}_0 \int^{\pi/3}_0 \int^2_{sec\phi} 3p^2sin\phi $ $ dp $ $ d\phi $ $ d\theta $ =$\int^{2\pi}_0 \int^{\pi/3}_0 (8-sec^3\phi)sin\phi $ $ d\phi $ $ d\theta $ =$\int^{2\pi}_0 [-8cos\phi-\frac{1}{2}sec^2\phi]^{\pi/3}_0 d\theta $ =$\int^{2\pi}_0[(-4-2)-(-8-\frac{1}{2})]d\theta $ =$\frac{5}{2}\int^{2\pi}_0 d\theta $ =$5\pi $
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