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 part of the disk $x ^ { 2 } + y ^ { 2 } \leq 1$ in the first quadrant and has density function p(x, y) = xy.

A) $\frac { 15 } { 8 }$

B) $\frac { 1 } { 5 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 1 } { 2 }$
E) $\frac { 8 } { 15 }$
F) $\frac { 1 } { 8 }$

G) $\frac { 5 } { 6 }$

H) 1