       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}}

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 . . .
>
>

```

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