       Re: piecewise definition of a function

• To: mathgroup at smc.vnet.net
• Subject: [mg43888] Re: piecewise definition of a function
• From: bobhanlon at aol.com (Bob Hanlon)
• Date: Fri, 10 Oct 2003 03:05:56 -0400 (EDT)
• References: <bm2ub8\$6s1\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

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

Plot[f[x], {x,-1,2}];

Integrate[f[x], {x,-50, 50}]

1

Bob Hanlon

In article <bm2ub8\$6s1\$1 at smc.vnet.net>, Nathan Moore <nmoore at physics.umn.edu>
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?

```

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