hmmm any ideas how to go about doing this integral (without a computer...)?

 

[math] \int^t_0e^{-\tau} \frac{1}{\sqrt{\tau}}d\tau [/math]

 

i tried Integration by parts but that seems to end up in me going roudn in circles for 5 hours!

 

thanks

 

Sarah

May I suggest you post what you have tried so far? Maybe then the experts can point you in the right direction

 

Also, have a lok at this, it seems to have examples that are simmilar to yours

 

Cheers,

 

Ryan Jones

This is the 'error function' (that is why it is called 'erf') modulo an overall factor of [math]\pi[/math]. It doesn't have a closed form but you can find an expansion for various limits (e.g. t large or t small) using integration by parts.

 

You can find more info here:

http://mathworld.wolfram.com/Erf.html

yeah the answer is [math] \sqrt{\pi} Erf (\sqrt{t}) [/math]

 

but i can't seem to get there, this is what i have done so far:

 

[math] \int^t_0e^{-\tau} \frac{1}{\sqrt{\tau}}d\tau [/math]

 

IBP gives:

 

[math] 2e^{-t} \sqrt{t} + 2 \int_0^te^{-\tau}\tau^{1/2} d\tau [/math]

 

but this seems to end up getting me nowhere....

these problems almost always work out very nicely via a change of variables. The definition of erf should give a very large clue as to what change should be made.

do you mean something like [math] \tau = x^2 [/math] ??

ah yep i see now, lol, so simple, but so hard to see!

 

thanks for the help guys!