Answer
$3.758\text{ uni}{{\text{t}}^{3}}$
Work Step by Step
\[\begin{align}
& f\left( x \right)={{e}^{-{{x}^{2}}}},\text{ }y=0,\text{ }x=-1,\text{ }x=1 \\
& \text{Using the disk method} \\
& V=\int_{-1}^{1}{\pi {{\left( {{e}^{-{{x}^{2}}}} \right)}^{2}}dx} \\
& \text{By symmetry} \\
& V=2\pi \int_{0}^{1}{{{e}^{-2{{x}^{2}}}}dx} \\
& \text{Integrating by a CAS }\left( \text{Wolfram Alpha Website} \right) \\
& V\approx 3.758\text{uni}{{\text{t}}^{3}} \\
\end{align}\]
