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

Multiple Choice

Solve the problem.
-Find the centroid of the infinite region in the first quadrant bounded by the coordinate axes and the curve $y = e ^ { - 4 x }$ .

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