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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.

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  • Re: Re: Help: ratio of integral of f(x)^2 to square of integral of f(x)
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>