Help finding ellipsoid volume with antiderivative?

Hi, I'm stuck on a homework problem and would appreciate some help, because it's getting late. :-(

I have to integrate x^2/a^2=y^2/b^2=1 for the volume of this ellipsoid rotating about the x-axis. I have -a<x<a (supposed to be less than or equal to but I don't have that key?) and -b<y<b (also less than or equal to).

How do I do the Remiens sum to get to the integral problem? We're supposed to do this with the antiderivative method.

I've got a half ellipse drawn & trying to do the disks, but I'm really stuck.

I get y=sqare root of b^2(1-x^2/a^2).

Thanks,

Jen