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!

Integrate X²e^-x²

  1. Feb 17, 2008 #1
    I am working on an integral I am finding tricky, and I think I'm missing something.
    I need to integrate on the interval 0 to infinity, x²e^-x².
    We have proved that on the interval of -∞ to ∞, e^-x²=√∏ so from o to ∞, it equals √∏/2. I can use this in my proof, but I don't see how. When I try integrating by parts I have trouble getting a finite answer. I would love some help,
  2. jcsd
  3. Feb 17, 2008 #2
    Try integrating by parts the

    [tex]I=\int_0^\infty e^{-x^2}\,d\,x[/tex]
  4. Feb 17, 2008 #3
    HOw can one integrate this by parts, i do not think this has any closed form does it?
  5. Feb 17, 2008 #4
    and this question is already on another forum!lol
  6. Feb 17, 2008 #5
    Like this:

    [tex]I=\int_0^\infty e^{-x^2}\,d\,x=\int_0^\infty (x)'\,e^{-x^2}\,d\,x[/tex]



    by OP
  7. Feb 17, 2008 #6
    At what level is one supposed to learn how to integrate this?? I mean where is it covered?
    Becasue this is my first time seeing such a trick!
  8. Feb 17, 2008 #7
    Did you read the original post????
    They gave him the result [itex]I=\frac{\sqrt{\pi}}{2}[/itex].

    As for the actual calculation, there are many ways to calulate [itex]I[/itex]. The simplest one is by double integrals.
  9. Feb 17, 2008 #8
    my fault

    i posted in the other forum before finding this one which I think may be more appropriate.
  10. Feb 17, 2008 #9
    Well, i did not read the op's post!
    and as for evaluating that integral, i think i should wait a few more months.
  11. Feb 17, 2008 #10
    ok then, like Hurky said, show what u did so far???
  12. Feb 17, 2008 #11
    I'm studying improper integrals for a "topics in advanced math" course. . .the proof is lengthy and involves double integrals and polar coords
  13. Feb 17, 2008 #12
    AH, i have never worked with double integrals, so i guess i cannot be of any further help, but surely the other guys will give u enough hints to get it right!
    good luck!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Integrate X²e^-x²
  1. Integral with e (Replies: 8)

  2. Integration (e) (Replies: 7)

  3. Integrate e (Replies: 2)

  4. Integrals with e (Replies: 4)

  5. Integration of e (Replies: 2)