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Math Help - Volumes of Solids of Revolution - Integration

  1. #1
    Newbie khanim's Avatar
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    Cool Volumes of Solids of Revolution - Integration

    I hope this in the correct section, admin please move it if its not

    Determine the volume generated when the given plane figure is rotated about the y axis

    x^2 - y^2 = 16

    y=0 x=8

    I'm having a problem with the integration part of it
    Please help
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by khanim View Post
    I hope this in the correct section, admin please move it if its not

    Determine the volume generated when the given plane figure is rotated about the y axis

    x^2 - y^2 = 16

    y=0 x=8

    I'm having a problem with the integration part of it
    Please help
    By definition: V = \pi \int_{y = 0}^{y = 8} x^2 \, dy.

    Substitute x^2 = 16 + y^2 into the integral. I don't see where the trouble can be ....?
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  3. #3
    Senior Member DeMath's Avatar
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    Quote Originally Posted by mr fantastic View Post
    By definition: V = \pi \int_{y = 0}^{y = 8} x^2 \, dy.

    Substitute x^2 = 16 + y^2 into the integral. I don't see where the trouble can be ....?

    Maybe do you mean this V = \pi \int\limits_0^{4\sqrt 3 } {\left( {64 - \left( {16 + {y^2}} \right)} \right)dy} ??
    Last edited by DeMath; October 2nd 2009 at 08:34 AM. Reason: The first time I wrong understood the conditions of the problem
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