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Math Help - volume of a solid of revolution?

  1. #1
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    volume of a solid of revolution?

    hello. i am not quite sure how to solve these problems when they aren't revolving around the x or y axis. for example:

    area within y=x^4 , y=1

    revolving around y=8

    What do I do?
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  2. #2
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    Quote Originally Posted by thedoge View Post
    hello. i am not quite sure how to solve these problems when they aren't revolving around the x or y axis. for example:

    area within y=x^4 , y=1
    Revolving x^4 about line y=1.

    Is the same as revolving x^4-1 about the line y=0 (x-axis). Think of this as a picture.

    Thus,
    \pi \int_{-1}^1 (x^4-1)^2 dx
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  3. #3
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    Well, that's what I thought too, but apparently my answer is wrong.
    Came out to 4.4680?
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  4. #4
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    Try using shells.

    2{\pi}\int_{0}^{1}(x-8)(x^{4}-1)dx
    Last edited by galactus; November 24th 2008 at 06:39 AM.
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