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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- From: "Carl K. Woll" <carlw@wolfram.com>
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