Volume of Ellipse No idea how to do this

[ruri]

Homework Statement

Rotating the ellipse x^2/a^2 + y^2/b^2 = 1 about the x-axis generates and ellipsoid. Compute its volume.

Homework Equations

The Attempt at a Solution

 

[grief]

You can do it several ways. One way to do it is to observe that if you rotate only the upper half of the ellipse you still get the same ellipsoid. Then slice it vertically. What is the positive value of y for each x? The rotation of each slice will be a disc. Integrate the volume of the discs to get the entire volume of the ellipsoid.