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Help with integration!

  1. Sep 21, 2010 #1
    Hi everyone,

    I am new to Physics Forums so please excuse me - I am so embarrassed that I can't do this integral, but its quite urgent and so if anyone here could help me I would be much obliged!

    The integral I must carry out is:

    [tex] \int_{-\infty}^{\infty}e^{-ax^{2}}\,\text{cos}kx\,dx [/tex]

    I already know that the solution is

    [tex] \sqrt{\frac{\pi}{a}}e^{-k^{2}/4a} [/tex]

    But the task is to find out how one can get to this answer...I think the hint is in:

    [tex] \int_{-\infty}^{\infty}e^{-ax^{2}}\,dx =\sqrt{\frac{\pi}{a}} [/tex]

    which is from the standard Gaussian distribution.

    Any information would be much appreciated!

    Thank you,
    Bladibla.
     
  2. jcsd
  3. Sep 21, 2010 #2
    Try integration by parts, twice.
     
  4. Sep 22, 2010 #3
    Hi zhermes, could you please be a little more specific? Thanks!
     
  5. Sep 22, 2010 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    That's not it. What you want to do is write cos(kx)=(e^(ikx)+e^(-ikx))/2. Combine the exponentials. You get integrands like exp(-a*(x^2+i*x*k/a)), right? You can complete the square and change variables.
     
  6. Sep 22, 2010 #5
    Hi Dick,

    Thank you so much!!

    Warm regards,
    Bladibla.
     
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