Example 2. Find the volume of the solid of revolution formed by rotating the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ around the $x$-axis.
If we take $s_{1}=s_{2}=0, s_{0}=\pi a b, h=2 b$ we get $V=\frac{2 b}{6}(0+4 \pi a b+0)=\frac{4}{3} \pi a b^{2}$. Or if we take $s_{1}=s_{2}=0, s_{0}=\pi b^{2}, h=2 a$ we get $\boldsymbol{V}=\frac{2 a}{6}\left(0+4 \pi b^{2}+0\right)=\frac{4}{3} \pi a b^{2}$. (Verification using definite integral is completely correct)