Re: piecewise definition of a function

*To*: mathgroup at smc.vnet.net*Subject*: [mg43897] Re: piecewise definition of a function*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>*Date*: Fri, 10 Oct 2003 03:06:14 -0400 (EDT)*References*: <bm2ub8$6s1$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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? There may be more than one "proper" technique. Using version 5, if you define your function to be either UnitStep[x] - UnitStep[x - 1] or If[0 < x < 1, 1, 0] the integration evaluates to 1, as desired. David Cantrell