Answer:

Step-by-step explanation:
First thing I did was graph this on my calculator to find the upper and lower bounds. They were x = 5, 9. Then I applied the disk method of integration. From this I know know I use y = x equations, x intervals, I need a value for R, and then I need a value for r. R represents the height of the representative rectangle which is perpendicular to the axis of rotation, so the height of that rectangle starts at y = 0 and meets the curve. So

Since there is no "hole" or space between the graph and the axis of rotation, r=0. Putting that into the volume formula:
![V=\pi \int\limits^9_5 {[-x^2+14x-45]^2-[0]^2} \, dx](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint%5Climits%5E9_5%20%7B%5B-x%5E2%2B14x-45%5D%5E2-%5B0%5D%5E2%7D%20%5C%2C%20dx)
To simplify I have to multiply that polynomial by itself. Doing that gives us:

Integrating gives us:
which we integrate from 5 to 9
Doing a bit of simplification on that:
from 5 to 9
Applying the First Fundamental Theorem of Calculus we get that when we sub in a 9 for x then a 5 for x:

which subtracts to
