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# 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

$\cfrac { 1 }{ 2 } \displaystyle\int_{ 0 }^{ \cfrac{\pi}{6} }{ \left( \cos 3\theta \right) ^{ 2 }d\theta }$

B

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

C

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

D

$3\displaystyle\int_{0}^{\cfrac{\pi }{6}} \cos(6\theta )d\theta$