Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solve this integral

  1. Nov 6, 2005 #1
    --------------------------------------------------------------------------------
    how do i get to solve this integral,i have no idea whatsoever so no one should expect what i have done.it was presented to me by a colleague
    [x^(1/x)]^[x^(1/x)]^[x^(1/x)]^[x^(1/x)]^[x^(1/x)]^[x^(1/x)]^[x^(1/x)]............
     
  2. jcsd
  3. Nov 6, 2005 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Do you mean the integral of that function?
    Do you have any reason to believe that function is well-defined, much less integrable?
    Does your colleague have a penchant for pulling your leg?

    A couple of points: since [itex][x^a]^b= x^{ab}[/itex], [itex][x^{\frac{1}{x}}]^{x^{\frac{1}{x}}}= x^{\frac{2}{x}}[/itex]. In general then, that "stack" of [itex]x^{\frac{1}{x}}[/itex], n times, is the same as [itex]x^{\frac{n}{x}}[/itex] and I see no reason to think that expanding it to infinity will give a function.
     
  4. Nov 6, 2005 #3

    benorin

    User Avatar
    Homework Helper

    Power Tower

    This is not well defined, it seems. Consider that [itex]e^{x^{2}}[/itex] is not the same as [itex]\left(e^{x}\right)^{2}=e^{2x}[/itex]. The one way to look at the given function is as a power tower (e.g. [tex]x^{x^{x^{x^{\cdot^{\cdot^{\cdot}}}}}}}[/tex],) see http://mathworld.wolfram.com/PowerTower.html for a reference; and another way is as HallsofIvy pointed out. I suppose it would depend on how, that is, by what limiting process, the given integrand is being defined. You might try defining the function as a limit of a sequence of functions, perhaps you can use the Lebesgue's Dominated Convergence Theorem to show convergence of the integral (supposing it's a definite one).
     
  5. Nov 6, 2005 #4
    i get the feeling that's a bull**** integral that the 'colleague' gave out....
     
  6. Nov 6, 2005 #5

    benorin

    User Avatar
    Homework Helper

    Why? Do you suppose it is homework?
     
  7. Nov 7, 2005 #6
    But Cant The Function Be Resolved To A Definite One That Can Be Integrable
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Solve this integral
  1. Solve this integral (Replies: 3)

Loading...