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: 65

Answer

$\frac{3}{4}$

Work Step by Step

We calculate the average as: average=$\frac{1}{(\frac{4\pi}{3})}\int^{2\pi}_0 \int^\pi_0 \int^1_0 p^3 sin\phi $ dp $ d\phi $ $ d\theta $ =$\frac{3}{16\pi} \int^{2\pi}_0 \int^{\pi}_0 sin\phi d\phi d\theta $ =$\frac{3}{8\pi} \int^{2\pi}_0 d\theta $ =$\frac{3}{4}$
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