Re: piecewise definition of a function
- To: mathgroup at smc.vnet.net
- Subject: [mg43892] Re: piecewise definition of a function
- From: poujadej at yahoo.fr (Jean-Claude Poujade)
- Date: Fri, 10 Oct 2003 03:06:02 -0400 (EDT)
- References: <bm2ub8$6s1$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Nathan Moore <nmoore at physics.umn.edu> wrote in message news:<bm2ub8$6s1$1 at smc.vnet.net>...
> I'd like to define a function in a piecewise manner. As of yet I've
> been unsuccessful with even the simplest example. Consider the
> following:
> first define a 1-d bump,
> f[x_] = If[x < 0, 0,If[x > 1, 0, 1]]
> Mathematica doesn't seem to mind this, as f[0.1] evaluates 1 and
> f[-23] evaluates 0.
> The problem comes when I try to integrate the function. The
> following command which should evaluate to 1 doesn't work AT ALL!
> Integrate[f[x], {x, -50, 50}]
[...]
If you use UnitStep it does work :
g[x_] := UnitStep[x] - UnitStep[x - 1];
Integrate[g[x], {x, -50, 50}]
1
---
jcp
ps : I don't know the reason why it doesn't work with If...