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Help me please

  1. Oct 15, 2008 #1
    hiiii

    can any body help me in solving this problem

    please help me as soon as possible


    [​IMG]



    thanks alot

    Moderation Note: Edited irritating title.
     
    Last edited by a moderator: Oct 15, 2008
  2. jcsd
  3. Oct 15, 2008 #2

    cristo

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    Re: help me pleeeeeeeeeeease

    You need to show some work before we can help you. What happened to the homework posting template?
     
  4. Oct 16, 2008 #3
    [​IMG]

    Read about Gamma function.
     
  5. Oct 16, 2008 #4
    thanks Alexitron

    you help me alot

    I'm now reading on Gamma function.





    regards.....
     
  6. Oct 16, 2008 #5

    HallsofIvy

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    To do this specific integral, you don't need the Gamma function.

    If
    [tex]I= \int_{-\infty}^\infty e^{-\frac{t^2}{2}} dt[/tex]
    then, because of the symmetry,
    [tex]\frac{I}{2}= \int_0^\infty e^{-\frac{t^2}{2}}dt[/tex]
    which also means that
    [tex]\frac{I}{2}= \int_0^\infty e^{-\frac{x^2}{2}}dx[/tex]
    and
    [tex]\frac{I}{2}= \int_0^\infty e^{-\frac{y^2}{2}}dy[/tex]
    so that
    [tex]\frac{I^2}{4}= \left(\int_0^\infty e^{-\frac{x^2}{2}}dx\right)\left( \int_0^\infty e^{-\frac{y^2}{2}}dy\right)[/tex]
    That can be interpreted as a double integral over the first quadrant of the plane and changing to polart coordinates gives an easy integral.
     
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