Solve the Problem $y = e ^ { - 4 x }$

Multiple Choice

Solve the problem.
-Find the center of mass of a thin infinite region in the first quadrant bounded by the coordinate axes and the curve $y = e ^ { - 4 x }$ if $\delta ( x , y ) = x y$ .

A) $\bar { x } = \frac { 1 } { 6 } , \bar { y } = \frac { 2 } { 9 }$
B) $\bar { x } = \frac { 1 } { 4 } , \bar { y } = \frac { 8 } { 27 }$
C) $\bar { x } = \frac { 1 } { 4 } , \bar { y } = \frac { 2 } { 9 }$
D) $\bar { x } = \frac { 1 } { 6 } , \bar { y } = \frac { 8 } { 27 }$