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AP® Calculus AB-BC

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Moderate

Area In Quadrant 1

APCALC-LJOPH8

Find the correct expression for the area of the enclosed region between the polar curve $r=1-2\cos { \theta }$ and the $y$-axis in quadrant I.

A

$\int _{ 0 }^{ \frac { \pi }{ 2 } }{ ( 1-2\cos { \theta } ) ^{ 2 }d\theta }$

B

$\cfrac { 1 }{ 2 } \int _{ 0 }^{ \frac { \pi }{ 2 } }{ ( 1-2\cos { \theta } ) ^{ 2 }d\theta } $

C

$\int _{ \frac { \pi }{ 3 } }^{ \frac { \pi }{ 2 } }{ ( 1-2\cos { \theta } ) ^{ 2 }d\theta } $

D

$\cfrac { 1 }{ 2 } \int _{ \frac { \pi }{ 3 } }^{ \frac { \pi }{ 2 } }{ ( 1-2\cos { \theta } ) ^{ 2 }d\theta } $