Find the Volume of the Solid Obtained by Rotating About $y = e ^ { - x ^ { 2 } } , y = 0 , x = 0$

Multiple Choice

Find the volume of the solid obtained by rotating about the y axis the region bounded by the curves. $y = e ^ { - x ^ { 2 } } , y = 0 , x = 0$ and $x = 9$

A) $V = \pi \left( \frac { 1 } { e ^ { 81 } } \right)$
B) $V = \pi \left( 1 - \frac { 1 } { e ^ { 81 } } \right)$
C) $V = \pi e ^ { 81 }$
D) $V = \pi \left( \frac { 1 } { e ^ { 81 } } - 1 \right)$
E) $V = \pi \left( e ^ { 81 } - 1 \right)$