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2 part washer method?

  1. Oct 11, 2011 #1
    1. The problem statement, all variables and given/known data

    I need to find the volume of the solid formed when rotating f(x) = 4x-x^2 and y=4 and x=0 about the y-axis.

    Using the disc/washer method.

    2. Relevant equations

    v = pi * integral from a to b of (r^2) * thickness

    3. The attempt at a solution

    I already did it using the shell method and got 128/3 pi.

    I am getting confused on how to do this, I believe it will need to be setup in 2 parts? Refer to my image sketch:

    [PLAIN]http://k.minus.com/je3SvPydQUFsp.png [Broken]

    Where I think the 2 parts are split by x=2. From x=0 to x=2 I see a disc method and then from x =2 to x=4 I see the washer method. However because the disc/washer method is perpendicular to the axis of rotation (y) that means that the thicknes of the disc/washers will be dy, which means the limits of integration would be in terms of y. Therefore I don't see how I can set it up with 2 equations with different integrals.
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Oct 11, 2011 #2


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    The volume is formed by rotation about the x-axis. The disks/washers should be vertical, not horizontal.

    They should be washers for this problem.
  4. Oct 12, 2011 #3
    Sorry it is about the y-axis , it was a mistype in the question on my part.
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