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Math Help - Volume :S blah

  1. #1
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    Volume :S blah

    I find it really hard trying to imagine what the picture is after rotation! :S Help please!



    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

    about the axis
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by MathNeedy18 View Post
    I find it really hard trying to imagine what the picture is after rotation! :S Help please!



    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

    about the axis

    use method of cylindrical shells:

    V= \int_a^b 2\pi x f(x) \, dx, since it is rotated on the y-axis..

    interval: [0,8]
     <br />
f(x) = x(8-x) = 8x-x^2<br />

    so, if we substitute these infos, we have V= \int_0^8 2\pi (8x^2 - x^3) \, dx
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