Sarahisme Posted May 18, 2006 Share Posted May 18, 2006 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 Link to comment Share on other sites More sharing options...
RyanJ Posted May 18, 2006 Share Posted May 18, 2006 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 Link to comment Share on other sites More sharing options...
Severian Posted May 18, 2006 Share Posted May 18, 2006 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 Link to comment Share on other sites More sharing options...
Sarahisme Posted May 19, 2006 Author Share Posted May 19, 2006 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.... Link to comment Share on other sites More sharing options...
Bignose Posted May 19, 2006 Share Posted May 19, 2006 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. Link to comment Share on other sites More sharing options...
Sarahisme Posted May 19, 2006 Author Share Posted May 19, 2006 do you mean something like [math] \tau = x^2 [/math] ?? Link to comment Share on other sites More sharing options...
Sarahisme Posted May 20, 2006 Author Share Posted May 20, 2006 ah yep i see now, lol, so simple, but so hard to see! thanks for the help guys! Link to comment Share on other sites More sharing options...
Recommended Posts
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!
Register a new accountSign in
Already have an account? Sign in here.
Sign In Now