Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 15: Multiple Integrals - Practice Exercises - Page 933: 30


$$\dfrac{ 3a}{4}$$

Work Step by Step

$I_{avg}=\dfrac{3}{4 \pi a^3} \int_0^{2\pi} \int_{0}^{\pi} \int_{0}^{a} \rho^3 \sin \phi d \ rho d \theta \\=\dfrac{3a}{16 \pi} \int_0^{2\pi} \int_{0}^{\pi} \sin \phi \ d \phi \ d\theta \\=\int_0^{2\pi} \dfrac{3a d\theta }{8\pi} \\= \dfrac{3a}{8\pi} \times (2\pi-0) \\=\dfrac{ 3a}{4}$
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