Volume of a solid using disk method

Question

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?

Answer 1

You have to integrate from -5 to 5 or multiply your integral by two. That does the trick

Answer 2

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