# Volume of a solid using disk method

I have the following homework problem which I can't seem to get right. The question stated is:

Find the volume of the solid generated by revolving the region bounded by the parabola $$y=\frac{x^2}{25}$$ and the line y=1 about the line y=1.

So I came up with the following integral and solved to get $$\frac{8}{3}\pi$$ but the correct answer according to my homework is $$\frac{16}{3}\pi$$. $$\pi\int_0^5\left(1-\frac{2x^2}{25}+\frac{x^4}{625}\right)dx$$

So is my integral correct and I'm simply not doing the math right when solving it? Or am I just missing something in the integral?

You forgot to multiple it by $$2$$, because you set the lower bound $$0$$ instead of $$-5$$.