Re: Integrate query
- To: mathgroup at smc.vnet.net
- Subject: [mg23386] Re: [mg23361] Integrate query
- From: Rob Pratt <rpratt at email.unc.edu>
- Date: Fri, 5 May 2000 02:07:21 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I'm calling the fraction p to avoid confusion with the function f.
Solve[Integrate[f[x], {x, 0, a}] == p]
For example,
Solve[Integrate[Exp[-x], {x, 0, a}] == 1/2]
Solve::"ifun": "Inverse functions are being used by \!\(Solve\), so some \
solutions may not be found."
{{a -> Log[2]}}
Rob Pratt
Department of Operations Research
The University of North Carolina at Chapel Hill
rpratt at email.unc.edu
http://www.unc.edu/~rpratt/
On Thu, 4 May 2000, A. E. Siegman wrote:
> I have a non-negative analytic function f[x] whose area (integral of
> f[x] from 0 to Infinity) is unity.
>
> I want to find the upper limit such that the integral up to that limit
> will contain a fixed fraction of the total area, i.e. find a such that
>
> Integrate[f[x], {x,0,a}] == f (f<=1)
>
> The question is, what's the most efficient way to program this, if I
> want to find a with fair accuracy, and with a variety of different
> functions f[x]?
>
> Thanks . . .
>
>