Re: integration frustration

*To*: mathgroup at smc.vnet.net*Subject*: [mg91926] Re: [mg91893] integration frustration*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Sat, 13 Sep 2008 05:53:53 -0400 (EDT)*References*: <200809120926.FAA28232@smc.vnet.net>

Replacedwings wrote: > Dear All, > > I have a question about a particular integral: > > > i[r]= Integrate[(L-z)(f[Sqrt[z^2+r^2]] -f[z]),{z,0,L}] > > Assumptions->f[0]==0, f[r]>0 if r>0. > > Is i[r]>=0 for all r? > > Any Ideas? > > Help! > > TIA, > > Chris Notice that your i[] is also a function of L. No, it is not always positive. Best way to show this is to construct a counterexample. Look for one that rises and then falls, so that your f[Sqrt[z^2+r^2]] will tend to be less than your f[z] (requires picking suitable f-dependent r to enforce this). If this is certifiably not homework, feel free to explain the application if you require an explicit counterexample. Daniel Lichtblau Wolfram Research

**References**:**integration frustration***From:*Replacedwings <cabaret_voltaire@hotmail.com>