The Center of Mass of a Lamina in the Shape $x ^ { 2 } + y ^ { 2 } = 1 , x \geq 0 , y \geq 0$

Multiple Choice

The center of mass of a lamina in the shape of a region in the xy-plane bounded by the $x ^ { 2 } + y ^ { 2 } = 1 , x \geq 0 , y \geq 0$ with area density $\rho ( x , y ) = x + y$ is

A) $\left( \frac { 3 ( 2 + \pi ) } { 16 } , \frac { 3 ( 2 + \pi ) } { 32 } \right)$
B) $\left( \frac { 3 ( 2 - \pi ) } { 32 } , \frac { 3 ( 2 - \pi ) } { 32 } \right)$
C) $\left( \frac { 3 ( 2 + \pi ) } { 32 } , \frac { 3 ( 2 + \pi ) } { 32 } \right)$
D) $\left( \frac { 3 ( 2 + \pi ) } { 32 } , \frac { 3 ( 2 - \pi ) } { 32 } \right)$
E) $\left( \frac { 3 ( 2 - \pi ) } { 32 } , \frac { 3 ( 2 + \pi ) } { 32 } \right)$