Re: Integral of Piecewise function involving DiracDelta

*To*: mathgroup at smc.vnet.net*Subject*: [mg74800] Re: Integral of Piecewise function involving DiracDelta*From*: dh <dh at metrohm.ch>*Date*: Thu, 5 Apr 2007 04:17:28 -0400 (EDT)*References*: <euvmuo$epv$1@smc.vnet.net>

Hi Andrew, Obviously there is a bug in the implementation of Pieceweise or its integral. Also note that: Integrate[Piecewise[{{DiracDelta[x],-1<x<1}},0],{x,-.1,.1}] evaluates to 1. Further, concerning your second question. It is well known that DiracDelta[a x] == DiracDelta[x] / a for a constant a>0. A handwaving argument is, that the dirac function becomes "narrower" by a factor of a, what makes the integral smaller by the same factor. Daniel Andrew Moylan 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 > >