Answer
$=\frac{1}{2}$
Work Step by Step
$r^{2}=sin2\theta$
or $r=\pm \sqrt {sin2\theta}$
Area enclosed by one loop is
$A=\frac{1}{2}\int_{0}^{\pi/2}(\sqrt {sin2\theta})^{2}d \theta$
$=\frac{1}{2}$
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: 18
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