I am very confused how to go about this problem:
Consider the solid obtained by rotating the region bounded by the given
curves about the x-axis:
y = 9 - 25x^2 , y = 0
Find the volume V of this solid.
I tried to do
integral from 0 to 9(pi(9 - 25x^2)^2)
but that doesnt seem to work out correctly.
You're on the right track. One issue: the function intersects $y=0$ when $x= \pm \frac 35$, not when $x=0$ and $x=9$.
So then we have $$\int_{-3/5}^{3/5} \pi (9 - 25x^2)^2 dx$$