1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Volume of the solid of revolution

  1. Jul 12, 2007 #1
    Find the volume of the solid of revolution obtained when the region under the graph of

    [tex]f(x) = \left( \frac{1}{x} \right) e^\frac{1}{x} [/tex]

    from x = 1 to x = 6

    2. Relevant equations

    [tex] \pi \int (f(x))^2 dx [/tex]

    3. The attempt at a solution

    Ok, the equation I gave above should be that of a definite integral with a=1 and b=6 (If anyone can tell me how to write that in Latex it would be much appreciated)

    So, the volume is

    [tex]\pi \int_1^6 \left( \frac{1}{x} \right) \left( e^\frac{1}{x} \right)^2 dx[/tex]

    So, we can simplyfy this to

    [tex]\pi \int_1^6 (x)^{-2} \times e^\frac{2}{x} dx[/tex]

    Now I'm a bit stuck as to where to go from here. Do I use the integration by parts method? I think I'm getting bogged down in unnecessary calculations. Can someone give me a hint or point me in the right direction?
    Last edited: Jul 12, 2007
  2. jcsd
  3. Jul 12, 2007 #2
    Try setting u = 1/x or something like that.
  4. Jul 12, 2007 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    ?? You didn't finish your sentence! Between what limits? Rotated around what axis?

    So you are rotating around the x-axis?

    And only the region between x= 1 and x= 6?

    No, If [itex]f(x)= \frac{1}{x}e^{1/x}[/itex] then both [itex]f^2(x)= \frac{1}{x^2}e^{2/x}[/itex]

    Okay, good. Now you have first x squared also. By the way, the code to put the limits of integration in is "\int_1^6". In other words, treat the lower limit as a subscript and the upper limit as a superscript on the integral sign.

    Looks to me like the substitution u= 2/x should work nicely.
  5. Jul 12, 2007 #4
    Many thanx for your time and help..... I've managed to solve using substitution as you suggested.
    Last edited: Jul 12, 2007
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Volume of the solid of revolution