Find the X-Coordinate of the Center of Mass of the Lamina

Multiple Choice

Find the x-coordinate of the center of mass of the lamina that occupies the region $D = \left\{ ( x , y ) \mid 0 \leq x \leq 1 , x ^ { 2 } \leq y \leq 1 \right\}$ and has density function p(x, y) = x + y.

A) $\frac { 6 } { 13 }$

B) $\frac { 7 } { 13 }$
C) $\frac { 8 } { 13 }$
D) $\frac { 9 } { 13 }$
E) $\frac { 6 } { 11 }$
F) $\frac { 7 } { 11 }$

G) $\frac { 8 } { 11 }$

H) $\frac { 9 } { 11 }$