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: 30

Answer

$\frac{64\pi^3}{27}$

Work Step by Step

We calculate the area as follows: $ A=\int^{2\pi}_0 \int^{4\theta/3}_0 rdr d\theta $ =$\frac{8}{9}\int^{2\pi}_0 \theta^2 d\theta $ =$\frac{64\pi^3}{27}$
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