Question involving the shell method

[tal444]

Homework Statement

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

Homework Equations

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

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?

 

[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 $x^2- 0= x^2$.

 

[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.