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: 14

Answer

$\frac{4}{3}$

Work Step by Step

$\int^2_0 \int ^x_0 ydydx $ =$\int^{\pi/4}_0 \int^{2sec\theta}_0 r^2 sin \theta drd\theta $ =$\frac{8}{3}\int^{\pi/4}_0 tan\theta \sec^2\theta $ =$\frac{4}{3}$
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