Answer
$6a^2 \pi$
Work Step by Step
$\int_{0}^{2 \pi}dy=a\int_{0}^{2 \pi}(2cost-cos2t)(cost-cos2t)dt$
$=2a^2\int_{0}^{2 \pi}[cos2t+1+(\dfrac{cos4t+1}{4})-3(cost)(cos2t)]dt$
$=6a^2 \pi$
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 - Review - Exercises - Page 710: 30
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