Re: Help: ratio of integral of f(x)^2 to square of integral of f(x)
- To: mathgroup at smc.vnet.net
- Subject: [mg67364] Re: Help: ratio of integral of f(x)^2 to square of integral of f(x)
- From: ronnen.levinson at gmail.com
- Date: Tue, 20 Jun 2006 02:14:47 -0400 (EDT)
- References: <e7589k$l5d$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi folks. Sorry, I omitted a trailing exponent in my definition of r: r = (b-a) Integral[ f(x)^2 dx, {x, a, b} ] / Integral[ f(x) dx, {x, a, b} ]^2 I hope this correction makes my question clearer. Thanks, Ronnen. ronnen.levinson at gmail.com wrote: > 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.
- Follow-Ups:
- Re: Re: Help: ratio of integral of f(x)^2 to square of integral of f(x)
- From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
- Re: Re: Help: ratio of integral of f(x)^2 to square of integral of f(x)