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AP® Calculus AB-BC

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Moderate

Area of a Polar Region

APCALC-XYUESX

Which of the following expressions gives the total area enclosed by the polar curve $r=cos\left ( 3\theta \right )$ shown in the figure above?

A

$\cfrac{1}{2}\int_{0}^{\cfrac{\pi }{6}}\left ( cos3\theta \right )^{2}d\theta$

B

$3\int_{0}^{\cfrac{\pi }{6}}\left ( cos3\theta \right )^{2}d\theta$

C

$\int_{0}^{\cfrac{\pi }{6}}\left ( cos3\theta \right )^{2}d\theta$

D

$\cfrac{1}{2}\int_{0}^{\cfrac{\pi }{6}} cos(6\theta )d\theta$