Answer
$$\frac{\pi}{16}$$
Work Step by Step
Given: $r=sin4\theta$
$$A=\int_{0}^{\pi/4}\frac{( {sin4\theta})^{2}}{2}d \theta=\int_{0}^{\pi/4}\frac{1}{4}( {1-cos8\theta})d \theta=\frac{\pi}{16}$$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 10 - Parametric Equations and Polar Coordinates - 10.4 Areas and Lengths in Polar Coordinates - 10.4 Exercises - Page 713: 19
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