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Re: piecewise definition of a function


On 10/9/03 at 1:55 AM, nmoore at physics.umn.edu (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!

Try defining piecewise functions using UnitStep, i.e.

f[x_]:= UnitStep@x - UnitStep[x-1]
Integrate[f[x], {x, -10, 10}]
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