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 - 10.4 Exercises - Page 693: 30

Answer

$=\frac{3\pi}{2}-4$

Work Step by Step

$A=\int_{0}^{\pi/2}\frac{(1-cos\theta)^{2}}{2}d \theta$ $=\int_{0}^{\pi/2}\frac{(1-2cos\theta+cos^{2}\theta)}{2}d \theta$ $=\frac{1}{4}[3\theta-4sin\theta+\frac{1}{2}sin2\theta]_{0}^{\pi/2}$ $=\frac{3\pi}{2}-4$
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