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AP® Calculus AB-BC

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

B

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

C

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

D

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