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MathGroup Archive 2007

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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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