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Math Help - Find the volume

  1. #1
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    Find the volume

    x=1-y^4, x=0; about the x=9

    I drew a picture and I turned it as if it was y=1-x^4 being rotated about y=9 and I made into 2 sections.

    So I'd have:
    2\int_{0}^{1}\left( 2\pi (9-x)\left(1-x^4\right)\right)dx=\frac{412}{15}\pi

    Can someone tell if that's correct. I'm using webassign and I'm on my last try lol
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  2. #2
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    Re: Find the volume

    Hey amthomasjr.

    You said in your post two different things: rotating about x = 9 and then rotating about y = 9. Which one is it?

    Also what rotation method are you using? (Shell method? Other method?)

    The rotation should be something like integrating pi*y^2*dx or pi*x^2*dy with a shift in the function if you are not rotating around the x or y axes.
    Thanks from amthomasjr
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  3. #3
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    Re: Find the volume

    Rotating about the x = 9 is the problem. The other stuff is from me turning the picture I drew.
    I am using the shell method. Should I use something different?
    Last edited by amthomasjr; February 20th 2013 at 04:11 PM.
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  4. #4
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    Re: Find the volume

    Hint: Try shifting the function to the origin and then use the normal formula for rotating about the x (or y depending on the problem) axis.
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  5. #5
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    Re: Find the volume

    I spent some more time on the problem this morning and I finally figured it out. I should have been using the washer method.

    2\int_{0}^{1} \pi\left[9^2-(9-(1-y^4))^2\right]dy=2\pi \int_{0}^{1}\left[81-(8+y^4)^2\right]dy=2\pi \int_{0}^{1}\left[17-16y^4-y^8\right]dy=\frac{1232}{45}\pi
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