Hello, mollymcf2009!

Given the region bounded by: .

Use the method of cylindrical shells to find the volume of the solid

obtained by rotating the region about the -axis.

We have a parabola: .

. . The vertex is and it opens to the right.

is a vertical line.

The graph looks like this: Code:

| | *
| *
| *:::|
| *::::::|
| *::::::::|
| (8,3)*:::::::::|
| *::::::::|
| *::::::|
| *:::|
| *
| | *
- - + - - - - - - - - - + - - - - - - -
| 9

The curves intersect at

The formula is: .

So we have: .

. . and we must evaluate: .