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Math Help - Volume of Revolution

  1. #1
    Senior Member polymerase's Avatar
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    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 y=x^3-4x and y=2-x about the line 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 2\pi(x+1) for circumference and dx for thickness. But i dont see hows its (2-x)-(x^3-4x) for height.

    Thanks
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  2. #2
    Eater of Worlds
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    Using shells, which is easiest because washers would mean we have to solve for x.

    2{\pi}\int_{-1}^{2}[(1+x)((x^{3}-4x)-(2-x))]dx
    Last edited by galactus; November 24th 2008 at 05:38 AM.
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  3. #3
    Senior Member polymerase's Avatar
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    Quote Originally Posted by galactus View Post
    Using shells, which is easiest because washers would mean we have to solve for x.

    2{\pi}\int_{-1}^{2}[(1+x)((x^{3}-4x)-(2-x))]dx
    shouldn't it be 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)
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  4. #4
    Eater of Worlds
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    Yes, you're correct. I just inadvertently typed it backwards. Sorry.
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