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Could anybody find an INTEGRAL?

  1. Nov 12, 2007 #1
    I've got a difficult integral, that is, [tex] \int_{-\infty}^{\infty} e^{\lambda x^{2}} dx [/tex]. Could anybody find its solution?
     
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  3. Nov 12, 2007 #2

    Doc Al

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  4. Nov 12, 2007 #3

    HallsofIvy

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    Since, for [itex]\lambda> 0[/itex], that is not bounded as x goes to infinity, and, if [itex]\lambda= 0[/itex], that is just [itex]\int_{-\infty}^{\infty} dx[/itex], neither of those exists.

    If, however, [itex]\lambda[/itex] is negative, It is well known that the integral is
    [itex]\sqrt{\pi/|\lambda |}[/itex].
     
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