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 . . . > >