Para encontrarmos o volume, realizaremos os cálculos abaixo:

\(\begin{align} & V=\int_{a}^{b}{\pi {{\left( f(x) \right)}^{2}}}dx \\ & V=\int_{-1,41}^{1,41}{\pi }{{\left( 2-{{x}^{2}} \right)}^{2}}dx \\ & V=\pi \int_{-1,41}^{1,41}{4-4{{x}^{2}}+{{x}^{4}}}dx \\ & V=\pi \left( 4x-4\frac{{{x}^{3}}}{3}+\frac{{{x}^{5}}}{5} \right)_{-1,41}^{1,41} \\ & V=\pi \left( \left( 5,64-3,7+1,1 \right)-\left( -5,64+3,7-1,1 \right) \right) \\ & V=\pi \left( (3)-\left( -3 \right) \right) \\ & V=6\pi \\ \end{align}\ \)

Portanto, o volume será de \(\begin{align} & V=6\pi \\ \end{align}\ \).