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Finding volume by integration

  1. Oct 7, 2013 #1
    Find the volume of the solid formed when the region bounded by the curves y=x3, y=1, and x=0 is rotated about the y-axis, use washer AND shell methods

    Disc/Washer:
    Ωx2dy = Ω(y1/3)2dy = Ωy2/3dy
    Volume:
    V = 0∫1 Ωy2/3dy = Ω{(3y5/3)/5} = 3Ω/5


    Shell:
    2Ωy(x)dx = 2Ωx(x3)dx = 2Ωx4dx
    Volume:
    V = 0∫1 2Ωx4dx = 2Ω{(x5)/5} = 2Ω/5


    Obviously this question seems simple enough but I'm finding different answers so I'm going wrong somewhere. Any help is appreciated
     
  2. jcsd
  3. Oct 7, 2013 #2

    LCKurtz

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    For a shell you want ##2\pi x(y_{upper}-y_{lower})## in the integrand. And use ##\pi## instead of ##\Omega##.
     
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