The Center of Mass of a Lamina in the Shape $x ^ { 2 } + y ^ { 2 } = 4 , x \geq 0 , y \geq 0$

Multiple Choice

The center of mass of a lamina in the shape of a region in the xy-plane bounded by $x ^ { 2 } + y ^ { 2 } = 4 , x \geq 0 , y \geq 0$ and x + y = 2 with area density $\rho ( x , y ) = x y$ is

A) $\left( \frac { 15 } { 28 } , \frac { 5 } { 8 } \right)$
B) $\left( \frac { 12 } { 5 } , \frac { 18 } { 5 } \right)$
C) $\left( \frac { 35 } { 22 } , \frac { 102 } { 77 } \right)$
D) $\left( \frac { 8 } { 5 } , \frac { 8 } { 5 } \right)$
E) $\left( \frac { 6 } { 5 } , \frac { 6 } { 5 } \right)$