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Homework Help: 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]

    and

    [tex]I=\frac{\sqrt{\pi}}{2}[/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!
     
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