The Center of Mass of a Lamina in the Shape $r = 2 + \cos ( \theta ) , 0 \leq \theta \leq \pi$

Multiple Choice

The center of mass of a lamina in the shape of a region in the xy-plane bounded by $r = 2 + \cos ( \theta ) , 0 \leq \theta \leq \pi$ and the polar axis with area density $\rho ( r , \theta ) = \sin \theta$ is

A) $\left( \frac { 15 } { 28 } , \frac { 5 } { 8 } \right)$
B) $\left( 0 , \frac { 21 } { 10 } \right)$
C) $\left( - \frac { 57 } { 44 } , 0 \right)$
D) $\left( \frac { 42 } { 65 } , \frac { 19 \pi } { 52 } \right)$
E) $\left( \frac { 8 } { 5 } , \frac { 8 } { 5 } \right)$