Find the Volume of the Solid Generated by Revolving the Region

Multiple Choice

Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve $y = e ^ { - 2 x }$ , and the line $x = 2$ about the $y$ -axis.

A) $\frac { 1 } { 2 } \pi \left( 1 - 5 \mathrm { e } ^ { - 4 } \right)$
B) $\frac { 1 } { 2 } \pi \left( 1 - 3 \mathrm { e } ^ { - 4 } \right)$
C) $\frac { 1 } { 2 } \pi \left( 1 - 4 \mathrm { e } ^ { - 4 } \right)$
D - $\frac { 1 } { 2 } \pi \left( 1 + 5 e ^ { - 4 } \right)$