Find the Center of Mass of a Thin Plate of Constant

Multiple Choice

Find the center of mass of a thin plate of constant density covering the given region.
-The region between the $x$ -axis and the curve $y = 5 \csc ^ { 2 } x , \frac { \pi } { 4 } \leq x \leq \frac { 3 \pi } { 4 }$

A) $\bar { x } = \frac { 3 \pi } { 8 } , \bar { y } = \frac { 20 } { 3 }$
B) $\bar { x } = \frac { \pi } { 2 } , \bar { y } = \frac { 15 } { 2 }$
C) $\bar { x } = \frac { \pi } { 2 } , \bar { y } = 5$
D) $\bar { x } = \frac { \pi } { 2 } , \bar { y } = \frac { 10 } { 3 }$