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Math Help - Trouble finding volume of shell

  1. #1
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    Trouble finding volume of shell

    Rotated about x-axis, shell method, y = 8, x = 0

    formula: 2pixy

    xy = x(x^3) = x^4
    integrate:
    x^4 = 1/5 x^5
    1/5(8)^5 = 6553.6
    *2 = 13107.2 pi

    answer should be 768/7 pi though.
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  2. #2
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    Re: Trouble finding volume of shell

    Hang on, which function are you trying to rotate?
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  3. #3
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    Re: Trouble finding volume of shell

    Quote Originally Posted by togo View Post
    Rotated about x-axis, shell method, y = 8, x = 0

    formula: 2pixy

    xy = x(x^3) = x^4
    I assume you mean that y= x^3 is being rotated about the x-axis. it would have been nice to say that!
    However, the formula is NOT "2pi xy". That would be correct is you were rotating the region above y= x^3, but for the region below, using the "shell method", each shell would be a cylinder with radius y and height 2- x, integrated with respect to y, not x. You want to integerate 2piy(2- x)dy.

    integrate:
    x^4 = 1/5 x^5
    No, x^4 is NOT equal to (1/5)x^5! Yes, of course, you mean that the integral of x^4 is equal to that (well, equal to (1/5)x^5+ C), but say that- don't write non-sense and depend on others to guess what you mean.

    1/5(8)^5 = 6553.6
    *2 = 13107.2 pi

    answer should be 768/7 pi though.
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  4. #4
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    Re: Trouble finding volume of shell

    ok. Yes the curve to rotate is y= x^3. I was tired when writing that post.
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