       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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