Answer
$=\frac{\pi}{16}$
Work Step by Step
$r=sin4\theta$
Area enclosed by one loop is
$A=\int_{0}^{\pi/4}\frac{( {sin4\theta})^{2}}{2}d \theta$
$=\int_{0}^{\pi/4}\frac{( {1-cos8\theta})}{4}d \theta$
$=\frac{\pi}{16}$
Multivariable Calculus, 7th Edition
by Stewart, James
Published by
Brooks Cole
ISBN 10:
0-53849-787-4
ISBN 13:
978-0-53849-787-9
Chapter 10 - Parametric Equations and Polar Coordinates - 10.4 Exercises - Page 693: 19
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