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Integral of exp(-kx^2)

  1. Jul 18, 2010 #1
    Hi there,
    what's the integral over infinity of exp(-kx^2 )? the integral of exp(-x^2) is sqrt(pi)...
    appreciate the help! I can't find the answer anywhere and can't work it out myself..
  2. jcsd
  3. Jul 18, 2010 #2


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    To integrate [itex]\int_{-\infty}^\infty e^{-kx^2} dx[/itex], let [itex]u= x\sqrt{k}[/itex] so that [itex]du= dx \sqrt{k}[/itex] and [itex]dx= du/\sqrt{k}[/itex].

    Your integral becomes
    [tex]\int_{-\infty}^\infty e^{-kx^2}dx= \frac{1}{\sqrt{k}}\int_{-\infty}^\infty e^{-u^2}du[/tex]
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