# Homework Help: Question involving the shell method

1. May 22, 2012

### tal444

1. The problem statement, all variables and given/known data
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the given axis:

y = x2, y = 0, x = 1, x = 2, about x = 1

2. Relevant equations

V = 2$\pi$$\int$xf(x)

3. The attempt at a solution

I am assuming based off the graph that my f(x) would be equal to 4-x2, but I am having difficulty figuring out the respective x value. Any help?

2. May 22, 2012

### HallsofIvy

Then I suggest you look at your graph again! Each shell, at a specific x, has a length ranging from y= 0 to $y= x^2$ so that its height is $x^2- 0= x^2$.

3. May 22, 2012

### tal444

Wow... that was silly of me. That makes a lot more sense. So I would integrate 2$\pi$$\int$(x-1)(x2)dx from 1 to 2, which gives me an answer of 17/2. Thanks for the help.