1. ## Volume of Revolution

I'm having trouble visualizing and putting together this concept.

Question: Find volume of solid generated by revolving the region bounded by $\displaystyle y=x^3-4x$ and $\displaystyle y=2-x$ about the line $\displaystyle x=-1$

So I want to use vertical cylindrical shells to find the volume. I know the general formula for a cylindrical volume is V=circumference x height x thickness. So i know it should be $\displaystyle 2\pi(x+1)$ for circumference and $\displaystyle dx$ for thickness. But i dont see hows its $\displaystyle (2-x)-(x^3-4x)$ for height.

Thanks

2. Using shells, which is easiest because washers would mean we have to solve for x.

$\displaystyle 2{\pi}\int_{-1}^{2}[(1+x)((x^{3}-4x)-(2-x))]dx$

3. Originally Posted by galactus
Using shells, which is easiest because washers would mean we have to solve for x.

$\displaystyle 2{\pi}\int_{-1}^{2}[(1+x)((x^{3}-4x)-(2-x))]dx$
shouldn't it be $\displaystyle 2{\pi}\int_{-1}^{2}[(1+x)((2-x)-(x^3-4x))]dx$?

but anyways...that does answer my question...about how you would set up the equation (ie. how to determine height of cylinders)

4. Yes, you're correct. I just inadvertently typed it backwards. Sorry.