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Double Integral

  1. Dec 5, 2008 #1
    1. The problem statement, all variables and given/known data

    The equation is [tex]\int^{t}_{0}[/tex]e[tex]^{-t'\gamma}[/tex][tex]\int^{t}_{0}[/tex]e[tex]^{t''\gamma}[/tex]f(t'')dt''dt'. f(t) is a random function with no known anti-derivative. I need to simplify this into a single integral of one variable.

    2. Relevant equations

    3. The attempt at a solution
    I moved the first exponential function inside the second integral but none of the regular properties of double integrals seem to work here. Does anyone have any ideas?
  2. jcsd
  3. Dec 5, 2008 #2


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    Science Advisor

    As written you have simply the product of two integrals,

    [tex]\left[\int^{t}_{0}e^{t'\gamma}dt' \right]
    \left[ \int^{t}_{0}e^{t''\gamma}f(t'')dt''\right][/tex]

    and the first one is simple.
  4. Dec 6, 2008 #3
    No, It's not a typo. I had no idea that that could be done. Thank you this makes this a lot easier.
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