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