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Homework Help: 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

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

    2Ωy(x)dx = 2Ωx(x3)dx = 2Ωx4dx
    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


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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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