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# Area of Inner Loop

APCALC-HLUVA1

Find the correct expression for the area of the inner loop of the polar curve $r=1-2\sin { \theta . }$

A

$\cfrac { 1 }{ 2 } \displaystyle\int _{ \frac { \pi }{ 6 } }^{ \frac { 5\pi }{ 6 } }{ ( 1-2\sin { \theta } ) ^{ 2 }d\theta }$

B

$\cfrac { 1 }{ 2 } \displaystyle\int _{ \frac { 5\pi }{ 6 } }^{ \frac { 13\pi }{ 6 } }{ ( 1-2\sin { \theta } ) ^{ 2 }d\theta }$

C

$\displaystyle\int _{ \frac { 5\pi }{ 6 } }^{ \frac { 13\pi }{ 6 } }{ ( 1-2\sin { \theta } ) ^{ 2 }d\theta }$

D

$\displaystyle\int _{ \frac { \pi }{ 6 } }^{ \frac { 5\pi }{ 6 } }{ ( 1-2\sin { \theta } ) ^{ 2 }d\theta }$