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MathGroup Archive 2006

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Help: ratio of integral of f(x)^2 to square of integral of f(x)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67352] Help: ratio of integral of f(x)^2 to square of integral of f(x)
  • From: ronnen.levinson at gmail.com
  • Date: Mon, 19 Jun 2006 00:01:20 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi.

I'm trying to determine whether the following ratio

r = (b-a) Integral[ f(x)^2 dx, {x, a, b} ] /
              Integral[ f(x) dx, {x, a, b} ]

is always greater than or equal to one for 0 < f(x) <= 1. All values
all real.

I've obtained r>=1 for all tested choices of f(x), but seek guidance to
find the general answer.

Yours truly,

Ronnen Levinson.

P.S. E-mailed CC:s of posted replies appreciated.


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