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

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.

y= 4x^{2}, y=-2x+6

2. Relevant equations

y= 4x^{2}, y=-2x+6

These 2 equations meet at x= -3/2 and x=1

integral from a to b of (2∏x*f(x)) dx

The answer is 250pi/3.

3. The attempt at a solution

Been spending over an hour with this and can't figure out a way to figure this out by shells. I can do this by discs and got the answer right. However, I want to figure this out by shells. First I drew the graph of these 2 equations to find where they meet at. I then did this:

[itex]\int^{-3/2}_{1}[/itex] 2[itex]\pi[/itex]x((-2x-6)-(4x^{2})) dx

I put this in Wolfram and I did not get the intended answer. I work this out by hand and I am getting something very different from Wolfram. Guidance please! Thanks in advance.

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# Volumes with Cylindrical Shell Method

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