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Homework Help: Help me please

  1. Oct 15, 2008 #1

    can any body help me in solving this problem

    please help me as soon as possible

    http://www.up3.cc [Broken]

    thanks alot

    Moderation Note: Edited irritating title.
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Oct 15, 2008 #2


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    Staff Emeritus
    Science Advisor

    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
    http://blue-whitegt.com/covers/Integral.JPG [Broken]

    Read about Gamma function.
    Last edited by a moderator: May 3, 2017
  5. Oct 16, 2008 #4
    thanks Alexitron

    you help me alot

    I'm now reading on Gamma function.

  6. Oct 16, 2008 #5


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    Science Advisor

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

    [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]
    [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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