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Math Help - Volume Around y-axis with Cylindrical Shells

  1. #1
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    Question Please help!!!~ about Volume Around y-axis with Cylindrical Shells

    The region R enclosed by the curves y=8 x-23 and y=-x2+20 x-50 is rotated about the y-axis. Use cylindrical shells to find the volume of the resulting solid.
    Last edited by shannon1111; May 28th 2009 at 11:47 AM.
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  2. #2
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    The Shell Method

    Okay, so r(x)=8x-23 and R(x)=-x^2+20x-50 Go ahead and set r(x)=R(x) and you get your bounds of integration, x=3\rightarrow9 . The shell method states that V=\int_a^b 2\pi x[R(x)-r(x)] dx = \int_3^9 2\pi x[(-x^2+20x-50)-(8x-23)] dx. Can you take it from there?
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