Re: piecewise definition of a function

• To: mathgroup at smc.vnet.net
• Subject: [mg43890] Re: [mg43870] piecewise definition of a function
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 10 Oct 2003 03:06:00 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```On Thursday, October 9, 2003, at 02:55 PM, Nathan Moore wrote:

> 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}]
>
> What is the proper technique here?
>
> Nathan Moore
> University of Minnesota Physics
>
>
>
The correct way to approach to do this in connection with integration
is by using the UnitStep function:

f[x_] := UnitStep[x]UnitStep[1 - x]

In[11]:=
Integrate[f[x],{x,-50,50}]

Out[11]=
1

Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/

```

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