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Homework Help: Volume generated by curve

  1. Jul 15, 2006 #1
    The question is

    Given a curve C whose equation is give by y=(12/(x + 3))- 4,
    find the region bounded by C, the line x=0, the line x=3 and the line y=8 is rotated through 360 degree about the y-axis. Calculate the exact value of the volume generated.

    My solution is here

    However, this solution is not the answer in the textbook. The anwser in the textbook is
    Can someone show me where am I doing wrong?
    Last edited: Jul 15, 2006
  2. jcsd
  3. Jul 15, 2006 #2


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    Homework Helper

    The error is in V1: Easy fix: [tex]V_1 = \pi 3^2 (2) - \pi (54 - 2 ln 2)[/tex].

    The volume you calculated is that of the solid generated by rotating the region between the given curve and the y-axis about the y-axis, but you wanted to rotate the region between the given curve and x=3 about the y-axis. So just subtract what you got for V1 from the volume of the cylinder of radius 3 with height 2.
  4. Jul 15, 2006 #3
    Awesome, very thanks=)
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