AP® Calculus AB-BC

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Moderate

Area of a Polar Region

APCALC-XYUESX

Created for Albert.io. Copyright 2017. All rights reserved.

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

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