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MathGroup Archive 2006

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Re: Evaluating integral with varying upper limit?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71051] Re: [mg71035] Evaluating integral with varying upper limit?
  • From: "Chris Chiasson" <chris at chiasson.name>
  • Date: Wed, 8 Nov 2006 06:10:31 -0500 (EST)
  • References: <200611060752.CAA08598@smc.vnet.net>

Try setting your AccuracyGoal and PrecisionGoal (and view the
definitions thereof if this is your first time using them ). You may
also want to enable arbitrary WorkingPrecision if you have high
Precision inputs (or exact inputs).

On 11/6/06, AES <siegman at stanford.edu> 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 . . .
>
>


-- 
http://chris.chiasson.name/


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