(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Set up the integral (do not evaluate) to find the volume by revolving the region enclosed by y=x^2-2x+2 and y=-x^2+6 about a) x = 3 and b) y = -5.

2. Relevant equations

Shell Method: V = 2∏ ∫ (radius)*(height)dx

Washer Method: V = ∏ ∫ (R^2 - r^2)dx

3. The attempt at a solution

I believe I need to use the Shell Method for part A.

V = 2∏ ∫ (-1→2) (3-x)*(-x^2+6-x^2+2x-2)dx

V = 2∏ ∫ (-1→2) (3-x)*(-2x^2+2x+4)dx

I believe I need to use the Disk/Washer Method for part B.

V = ∏ ∫ (-1→2) [(-x^2 +6+5)^2 - (x^2-2x+2+5)^2]dx

V = ∏ ∫ (-1→2) [(-x^2 +11)^2 - (x^2-2x+7)^2]dx

But I'm not sure. Rotating about the axes are a lot simpler and I'm not sure about how to handle the values for x < 0. In my head, I think the equations will handle that for me, but I'm concerned.

Thanks for the help.

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# Homework Help: Disk/Shell Method and Volume

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