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

>

>

```

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