The Center of Mass of a Lamina in the Shape $y = \sqrt { x }$

Multiple Choice

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

A) $\left( \frac { 15 } { 28 } , \frac { 5 } { 8 } \right)$
B) $\left( \frac { 12 } { 5 } , \frac { 18 } { 5 } \right)$
C) $\left( \frac { 15 } { 28 } , \frac { 5 } { 9 } \right)$
D) $\left( \frac { 1 } { 2 } , \frac { 16 } { 9 } \right)$
E) $\left( \frac { 35 } { 22 } , \frac { 102 } { 77 } \right)$