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## Homework Statement

Use the method of cylindrical shells to find the volume generated by rotation the region bounded by the given curves about the specified axis.

## Homework Equations

y = x^2, y = 2-x^2; about x = 1

## The Attempt at a Solution

I tried to just break it down.

I want something of the form 2∏rhΔr

OK so To find the height f(x) I subtracted.

2-x^2-x^2 = 2-2x^2. For the radius I did a-x so 1-x is the radius

So I have

V = 2∏∫ (1-x)(2-2x^2)dx between -1 and 1 because that is where the graphs intersect.

Evaluating it I got 2∏((x^4)/2 -(2x^3)/3 -x^2 +2x ] between -1 and 1

I got 16∏/3

Is this the right way?