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

Evaluation of an integral

  1. Apr 29, 2005 #1
    Does anyone know how to go about solving

    [itex]\int e^{(x^{2})} dx[/itex]
     
  2. jcsd
  3. Apr 29, 2005 #2
    not expressible in terms of elementary functions. Using the "special" function, [itex]\mbox{erf} (x)[/itex] (the "error function", defined by [itex]\mbox{erf}(x) = 2/\sqrt{\pi} \int_0^x e^{-t^2} \ dt[/itex]), you can express the integral in this way, though:

    [tex]\int e^{(x^2)} \ dx = -\frac{i\sqrt{\pi}}{2}\mbox{erf}(ix)+C.[/tex]

    Essentially what this means is that you either have to compute definite integrals with this integrand numerically, or look up values on tables for the error function.
     
  4. Apr 29, 2005 #3
    This is helpful. I have the bounds. Thaks. It is weird that there is no analytical solution to something that looks so simple. I did write a taylor series and integrated that to get an infinite sum that is equal to the integral. It is:

    [itex]
    \sum_{n=0}^{\infty} \frac{x^{2n+1}}{(2n+1)n!}}
    [/itex]
     
  5. Apr 29, 2005 #4
    that's like the classic example of something that has no elementary solution...
     
  6. Apr 30, 2005 #5

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    The "erf" function is tabulated for real arguments only...


    Daniel.
     
  7. Apr 30, 2005 #6
  8. Apr 30, 2005 #7

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Give me a link to the page in A & Stegun where the erf function of complex arg is tabulated.

    Daniel.
     
  9. Apr 30, 2005 #8

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...
Similar Threads for Evaluation integral Date
I Evaluation of a line integral Sep 14, 2017
I Evaluating improper integrals with singularities Mar 15, 2017
A Who can help evaluate this integral? Oct 10, 2016
I How to evaluate this integral? Aug 22, 2016
A Evaluation of a horrible Multiple Integral Apr 6, 2016