The Center of Mass of a Lamina in the Shape $y = x ^ { 2 }$

Multiple Choice

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

A) $\left( \frac { 27 } { 2 } , \frac { 81 } { 5 } \right)$
B) $\left( \frac { 6 } { 13 } , \frac { 190 } { 273 } \right)$
C) $\left( 2 , \frac { 3 } { 2 } \right)$
D) $\left( \frac { 3 } { 8 } , \frac { 17 } { 16 } \right)$
E) $\left( \frac { 6 } { 5 } , \frac { 9 } { 5 } \right)$