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Uncertain about volume of bounded region question

  1. Nov 14, 2009 #1
    1. The problem statement, all variables and given/known data

    The question states:

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

    The lines are, y=lnX, y = 1, y = 2, and x = 0, rotated about the y-axis.

    I know how to integrate it, I just don't exactly know which region I'm taking the volume of, so I am having trouble setting up the integration problem.

    I have provided a graph of the curves.

    http://img691.imageshack.us/img691/2071/boundregion.png [Broken]


    I think I got it, here's my attempt at the solution:

    I'm going to use the area of circles method going vertical. So I find the distance from the y-axis to the lnX curve, which is equal to [tex]e^y[/tex]. From there I do [tex]\int_{0}^{2}\pi(e^{2y})dy -\int_{0}^{1}\pi(e^{2y})dy[/tex]
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Nov 14, 2009 #2


    Staff: Mentor

    The region being revolved is bounded below by the line y = 1, above by the line y = 2, on the right by y = ln x, and on the left by the line x = 0. On your graph, this region has a roughly trapezoidal shape, and lies between the purple line and the light brown line. You first integral (it should include dy) gives you the volume of the rotated region.

    BTW, you are integrating by using disks, not circles.
  4. Nov 15, 2009 #3


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    Science Advisor

    And the disks are horizontal, not vertical.
  5. Nov 16, 2009 #4
    I meant that the disks are stacked on top of eachother vertically.
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