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What would the new limits be for this integral?

  1. Mar 29, 2014 #1
    I am working on an physics problem and it has boiled down to this integral.

    [tex]\int_{0}^{∞} r e^{-\frac{1}{2 r_0}(r-i r_0^2 q)^2}dr[/tex]

    I found that if I make the substitution ##u=r-i r_0^2 q##, then I can do the integration, but I am a little confused about what the limits would be in terms of u. Normally I would just replace u with its expression in terms of r, but one of the integrals turns out being a gaussian integral and thus, doesn't have an indefinite form.

    I have for the upper limit to be ∞, but the lower limit is ##-i r_0^2 q##. This lower limit obviously will not work for the gaussian integral. Plus it doesn't make sense to me, a negative, complex radial limit?
     
  2. jcsd
  3. Mar 30, 2014 #2

    Simon Bridge

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    $$\int_a^b f(x)dx = \int_{u(a)}^{u(b)}g(u)du$$

    I see... perhaps the way to make sense of it for you is to separate the integrand into real and imaginary parts before you do the substitution.

    You can also consider that u is not a radius.
     
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