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Homework Help: Volume using Cylindrical Shells

  1. Oct 10, 2011 #1
    1. The problem statement, all variables and given/known data

    Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves y = 4+3x-x^2 and y+x=4 about the y-axis. Below is a graph of the bounded region.

    2. Relevant equations

    V = ∫ a to b 2 pi x f(x)
    3. The attempt at a solution

    ∫from 0 to 4 2 pi (4-x)(4)

    ∫from 0 to 4 2 pi (16-4x)

    ∫ [16-4(4) - (16- 4(0))]

    0 - 12


    I'm not exactly sure how to come about this problem with cylindrical shells.
  2. jcsd
  3. Oct 10, 2011 #2


    Staff: Mentor

    Your relevant equation is right, but in your integral, you forgot the radius factor, x.

    [tex]2\pi \int_0^4 x(4x - x^2)dx[/tex]

    You can see the LaTeX I used by clicking the integral above.
  4. Oct 10, 2011 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Draw a graph. Where do those curves intersect?
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