Re: Evaluating integral with varying upper limit?

*To*: mathgroup at smc.vnet.net*Subject*: [mg71054] Re: Evaluating integral with varying upper limit?*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Wed, 8 Nov 2006 06:10:55 -0500 (EST)*References*: <eimqg9$b9k$1@smc.vnet.net>

It will be very helpful if you give your function f[x] Regards Dimitris AES wrote: > Given a function f[x] which happens to be rather messy and not > analytically integrable, I want to evaluate the function > > g[y_] := NIntegrate[f[x], {x, ymin, y} ] > > with ymin fixed and ymin < y < Infinity. > > I suppose that FunctionInterpolate is the way to go here (???). > > But, are there tricks to tell FunctionInterpolate what I know in > advance, namely that f[x] is everywhere positive, and decreases toward > zero rapidly enough at large x that g[y] will approach a finite limiting > value as y -> Infinity? (which value I'd like to have FI obtain with > moderate accuracy -- meaning 3 or 4 significant digits, not 10 or 20) > > Thanks . . .