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/