erf anyone? help please :P

[Sarahisme]

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

[RyanJ]

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

[Severian]

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

[Sarahisme]

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....

[Bignose]

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.

[Sarahisme]

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

[Sarahisme]

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

 

thanks for the help guys!