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 15.4 - Double Integrals in Polar Form - Exercises 15.4 - Page 893: 33



Work Step by Step

We calculate the average as follows: average=$\frac{4}{\pi a^2} \int^{\pi/2}_0 \int^{a}_0 r\sqrt{a^2-r^2}drd\theta $ =$\frac{4}{3\pi a^2}\int^{\pi/2}_0 a^3 d\theta $ =$\frac{2a}{3}$
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