Re: Integral of Piecewise function involving DiracDelta

• To: mathgroup at smc.vnet.net
• Subject: [mg74802] Re: [mg74769] Integral of Piecewise function involving DiracDelta
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Thu, 5 Apr 2007 04:18:30 -0400 (EDT)

The problem appears to be with the compound inequality.

Works if you use (-1 < x || x < 1) vice (-1 < x < 1)

\$Version

5.2 for Mac OS X (June 20, 2005)

Integrate[DiracDelta[x],{x,-Infinity,Infinity}]

1

Integrate[DiracDelta[x],{x,-1,1}]

1

Integrate[Piecewise[{{DiracDelta[x], -1 < x || x < 1}}, 0],
{x, -Infinity, Infinity}]

1

Integrate[DiracDelta[x-1/2],{x,-Infinity,Infinity}]

1

Integrate[DiracDelta[x-1/2],{x,-1,1}]

1

Integrate[Piecewise[{{DiracDelta[x - 1/2], -1 < x || x < 1}}, 0],
{x, -Infinity, Infinity}]

1

Bob Hanlon

---- Andrew Moylan <andrew.j.moylan at gmail.com> 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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