Integral of Piecewise function involving DiracDelta

*To*: mathgroup at smc.vnet.net*Subject*: [mg74769] Integral of Piecewise function involving DiracDelta*From*: "Andrew Moylan" <andrew.j.moylan at gmail.com>*Date*: Wed, 4 Apr 2007 04:09:41 -0400 (EDT)

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