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MathGroup Archive 2000

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Re: Integrate query

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23397] Re: [mg23361] Integrate query
  • From: Matt.Johnson at autolivasp.com
  • Date: Fri, 5 May 2000 02:07:39 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com


FindRoot should work...

FindRoot[ Integrate[ f[x] ==(fixed fraction), { x, 0, a }], {a, (initial guess)}
]

-matt





"A. E. Siegman" <siegman at stanford.edu> on 05/04/2000 12:59:28 AM

Subject: [mg23397]  [mg23361] Integrate query




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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