Need help setting up integral. (Doesn't have to be solved)

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Homework Statement


Set up a definite integral that could be evaluated to find the volume of the solid that results when the region enclosed by the curves y=(x^2)-1, x=2, and y=0 is revolved about the y-axis.
(doesn't have to be solved) I have look at my book for help and I'm stuck.
 
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What have you tried so far?

Please post your attempt and any rough work that pertains to this problem.
 
I've graphed it, but that still doesn't get me any where I don't know which integral to set it up with.
 
Ok this is what i got probably wrong. V=\pi (integral) [x2-1] dy

with the lower limit of the integral being 0 and the top being 2
 
What does the region that will be revolved around the y-axis look like? Have you drawn a sketch of the revolved solid. Are you going to use shells or disks to get the volume?

What expression represents your typical volume element?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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