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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



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