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$0^{6} $\int$0^{y} x dx dy = $\int$ \pi\div4 ^ \pi\div2 $\int$0 ^ 6cos theta r^ 2 cos theta dr d theta =72$ \int$ \pi /4 ^ pi /2 cot theta cos^ 2 theta d theta =-36[cot^ 2 theta ] pi /4 ^ pi /2 =36
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