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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)
*Reply-to*: hanlonr at cox.net
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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