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: 13

Answer

36

Work Step by Step

$\int ^6_0 \int ^y_0 xdxdy $ =$\int ^{\pi/2}_{\pi/4} \int ^{6csc\theta}_0 r^2 cos\theta drd\theta $ =72$\int ^{\pi/2}_{\pi/4} cot \theta csc^2\theta d\theta $ =-36[$ cot^2\theta $]$^{\pi/2}_{\pi/4}$ =36
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