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Find the Area of the Specified Region r=asinθr = a \sin \theta

Question 95

Multiple Choice

Find the area of the specified region.
-Inside the circle r=asinθr = a \sin \theta and outside the cardioid r=a(1sinθ) ,a>0r = a ( 1 - \sin \theta ) , a > 0


A) a26(6π) \frac { a ^ { 2 } } { 6 } ( 6 - \pi )
B) a26(4π33) \frac { a ^ { 2 } } { 6 } ( 4 \pi - 3 \sqrt { 3 } )
C) a23(33π) \frac { a ^ { 2 } } { 3 } ( 3 \sqrt { 3 } - \pi )
D) a212(2π33) \frac { a ^ { 2 } } { 12 } ( 2 \pi - 3 \sqrt { 3 } )

Correct Answer:

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