Find the volume of the solid generated by revolving about the x-axis the region bounded by the x-axis and the upper half of the ellipse

x^2/a^2 + y^2/b^2 = 1

(and thus find the volume of a prolate spheroid)

Here a and b are positive constants with a>b

Volume of the solid of revolution?

Okay, so this one is tripping me up a bit... here's what I've done:

I tried to solve for y and got --

y = square root(b^2(1 - x^2/a^2)) or y = b*sqrt(1 - x^2/a^2)

I thought I would need to square the function and ultimately multiply by pi:

pi int_a^b (b^2(1-x^2/a^2) dx and I moved the b^2 to the beginning with pi and integrated to get:

b^2* pi [ x - x^3/3a^2]

so my final answer, keeping the b and a...

b^2*pi[(b-(b^3)/(3a^2))-(a-(a^3)/(3a^2))]

unfortunately this is not the correct answer. any help?? thanks!