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Math Help - Porblem in a definite integral

  1. #1
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    Jun 2008
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    Porblem in a definite integral

    I have the following integral. I want to have its value for known value of t (say 10), but I cannot solve it because the inner integral cannot be solved. Is there any way to solve this? I don't know,May be by separation of integrals or some numerical method. I tried Mathematica and it cannot solve it too.

    \int_{0}^{t}\int_{0}^{\tau}\frac{1}{\sqrt{\tau-u} }Erfc(\frac{1}{2\sqrt u})dud\tau
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  2. #2
    Super Member
    Joined
    Aug 2008
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    I'm pretty sure Mathematica needs to know what tau is before it can increment u so we have to specify tau before u in NIntegrate:


    Code:
    f[t_] := NIntegrate[(1/Sqrt[\[Tau] - u])*Erfc[1/(2*Sqrt[u])], 
           {\[Tau], 0, t}, {u, 0, \[Tau]}];
    Double-check it though: is the value returned by NIntegrate what you expect?
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