# Porblem in a definite integral

• October 22nd 2008, 11:50 AM
Ehsan
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.

$\int_{0}^{t}\int_{0}^{\tau}\frac{1}{\sqrt{\tau-u} }Erfc(\frac{1}{2\sqrt u})dud\tau$
• October 22nd 2008, 01:06 PM
shawsend
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?