Find the Center of Mass of a Thin Plate Covering $x = y ^ { 2 }$

Multiple Choice

Find the center of mass of a thin plate covering the given region with the given density function.
-The region bounded by $x = y ^ { 2 }$ and the line $x = 1$ , with density $\delta ( x ) = y ^ { 2 }$

A) $\bar { x } = \frac { 5 } { 7 } , \bar { y } = 0$
B) $\bar { x } = 0 , \bar { y } = \frac { 3 } { 5 }$
C) $\bar { x } = \frac { 3 } { 5 } , \bar { y } = 0$
D) $\bar { x } = \frac { 3 } { 7 } , \bar { y } = 0$