Answer
$\dfrac{9}{2} \pi$
Work Step by Step
Here, $A=(2) \int_{0}^{\pi} (\dfrac{1}{2}) r^2 d\theta$
Then, $A=2 \int_{0}^{\pi} (2-\cos \theta)^2$
This implies that
$A=\int_{0}^{\pi} [4+\cos^2 \theta-4 (\cos \theta) ]d\theta=\dfrac{9}{2} \pi$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 11: Parametric Equations and Polar Coordinates - Practice Exercises - Page 688: 47
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