Solve the Problem $y$ -Axis of a Thin Infinite Region in the First Quadrant

Multiple Choice

Solve the problem.
-Find the moment of inertia about the $y$ -axis of a thin infinite region in the first quadrant bounded by the coordinate axes and the curve $y = e ^ { - 3 x }$ if $\delta ( x , y ) = x y$ .

A) $\frac { 1 } { 432 }$
B) $\frac { 1 } { 54 }$
C) $\frac { 5 } { 1296 }$
D) $\frac { 1 } { 135 }$