The Center of Mass of a Lamina in the Shape $\rho ( x , y ) = x ^ { 2 } + y ^ { 2 }$

Multiple Choice

The center of mass of a lamina in the shape of a region in the xy-plane bounded by the x-axis, x + y = 3 and the y-axis with area density $\rho ( x , y ) = x ^ { 2 } + y ^ { 2 }$ is

A) $\left( \frac { 6 } { 5 } , \frac { 6 } { 5 } \right)$
B) $\left( \frac { 27 } { 2 } , \frac { 79 } { 5 } \right)$
C) $\left( \frac { 23 } { 2 } , \frac { 81 } { 5 } \right)$
D) $\left( \frac { 25 } { 2 } , \frac { 81 } { 5 } \right)$
E) $\left( \frac { 21 } { 2 } , \frac { 81 } { 5 } \right)$