Find the volume of the spheroid formed by the revolution of the area bounded by the ellipse x^2/(a^2)+ y^2/(b^2)=1 about the major axis a.
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1. The axis a is placed on the x-axis.
A rotation volume with the x-axis as axis of rotation is calculated by: $\displaystyle V_{rotx} = \int (\pi \cdot y^2)dx$
2. Since you need y² solve the equation of the ellips for y² and use the formula from #1. The bounds of the integral are -a and a. (Why?)