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>
- integration frustration