Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 10 - Parametric Equations and Polar Coordinates - Review - Exercises - Page 710: 36


$\dfrac{51\sqrt 3}{16}$

Work Step by Step

$r=2 +cos 2 \theta$ and $r=2+sin \theta$ $Area,A= 2[\frac{1}{2}\int_{-\pi/2}^{\pi/6}(2 +cos 2 \theta)^2-( 2+sin \theta)^2]d\theta$ $=\int_{-\pi/2}^{\pi/6}\frac{cos 4\theta}{2}+4 cos 2 \theta+\frac{cos 2\theta}{2}-4 sin \theta d\theta$ $=[\frac{sin 4\theta}{8}+2 sin 2 \theta+\frac{sin 2\theta}{4}+4 cos \theta]_{-\pi/2}^{\pi/6}$ $=\dfrac{51\sqrt 3}{16}$
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