Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 10 - Parametric Equations and Polar Coordinates - Review - Exercises - Page 730: 35



Work Step by Step

$r=2 sin \theta$ and $r=sin \theta+cos \theta$ $Area,A= \frac{1}{2}\int_{0}^{\pi/4}2sin\theta)^2d\theta+\frac{1}{2}\int_{\pi/4}^{3\pi/4}(\sqrt 2sin( \theta+ \pi/4))^2d\theta$ $=[\theta-\frac{1}{2}sin 2\theta]_{0}^{\pi/4}+[\frac{1}{2} \theta -\frac{1}{4} sin (2 \theta+ \pi/2)]_{\pi/4}^{3\pi/4}$ $=\frac{\pi-1}{2}$
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