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Volumes of Revolution: Revolving about a vertical axis

  1. Jul 24, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the volume of the solid obtained by rotating the region under the graph of y=1/x and y=1/x^2 about the vertical axis x=-1

    Also given are points on the y-axis (0,2) and (0,5). I guessing these points are specific sections of the graphs where we find the volume.



    2. Relevant equations
    Volume of revolution = pi int_a^b ((R^2)-(r^2))dx


    3. The attempt at a solution
    For this problem I would think...
    a=2
    b=5
    but I am uncertain as to how to find R and r. I know they correspond the outer and inner radii but how do I go about find them.

    I attached a picture of what the problem looks like.
     

    Attached Files:

  2. jcsd
  3. Jul 25, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Not "under" the graphs, between them.

    Since you drew a picture of the curves, also draw the line x= 1 and imagine a horizontal line from from x= 1 to those curves, for a given y.

    You are rotating the outer graph, y= 1/x2, around the line x= 1. R is the distance between those two, for each y: 1- 1/x2. r, the inner radius, is the distance from the curve y= 1/x to 1: 1- 1/x.
     
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