Re: Integral of Piecewise function involving DiracDelta

*To*: mathgroup at smc.vnet.net*Subject*: [mg74802] Re: [mg74769] Integral of Piecewise function involving DiracDelta*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Thu, 5 Apr 2007 04:18:30 -0400 (EDT)*Reply-to*: hanlonr at cox.net

The problem appears to be with the compound inequality. Works if you use (-1 < x || x < 1) vice (-1 < x < 1) $Version 5.2 for Mac OS X (June 20, 2005) Integrate[DiracDelta[x],{x,-Infinity,Infinity}] 1 Integrate[DiracDelta[x],{x,-1,1}] 1 Integrate[Piecewise[{{DiracDelta[x], -1 < x || x < 1}}, 0], {x, -Infinity, Infinity}] 1 Integrate[DiracDelta[x-1/2],{x,-Infinity,Infinity}] 1 Integrate[DiracDelta[x-1/2],{x,-1,1}] 1 Integrate[Piecewise[{{DiracDelta[x - 1/2], -1 < x || x < 1}}, 0], {x, -Infinity, Infinity}] 1 Bob Hanlon ---- Andrew Moylan <andrew.j.moylan at gmail.com> wrote: > Here is an integral that I expect Mathematica to evaluate to 1: > > Integrate[Piecewise[{{DiracDelta[x], -1 < x < 1}}, 0], > {x, -Infinity, Infinity}] > > However, Mathematica 5.2 (Windows) gives the answer as 0. Here's a > similar integral that I also expect to evaluate to 1: > > Integrate[Piecewise[{{DiracDelta[x-1/2], -1 < x < 1}}, 0], > {x, -Infinity, Infinity}] > > For this integral, Mathematica doesn't return 0. It returns the > following: > > Integrate[Piecewise[{{2*DiracDelta[-1 + 2*x], -1 < x < 1}}, > 0], {x, -Infinity, Infinity}] > > Can anyone help me understand what's happening here? > > Cheers, > > Andrew > >