Solve the Problem $y = e ^ { - 2 x }$

Multiple Choice

Solve the problem.
-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 $x = 6$ about the $y$ -axis.

A) $\frac { 1 } { 2 } \pi \left( 1 - 13 \mathrm { e } ^ { - 12 } \right)$
B) $- \frac { 1 } { 2 } \pi \left( 1 + 13 \mathrm { e } ^ { - 12 } \right)$
C) $\frac { 1 } { 2 } \pi \left( 1 - 11 \mathrm { e } ^ { - 12 } \right)$
D) $\frac { 1 } { 2 } \pi \left( 1 - 12 \mathrm { e } ^ { - 12 } \right)$