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Re: Integral of Piecewise function involving DiracDelta

• To: mathgroup at smc.vnet.net
• Subject: [mg74781] Re: Integral of Piecewise function involving DiracDelta
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Thu, 5 Apr 2007 04:07:41 -0400 (EDT)
• References: <euvmuo$epv$1@smc.vnet.net>

For integrals like yours I would strongly suggest the
PiecewiseIntegrare function
by Maxim Rytin available from here:

http://library.wolfram.com/infocenter/MathSource/5117/

After loading the package, we get

In[54]:=
PiecewiseIntegrate[Piecewise[{{DiracDelta[x], -1 < x < 1}}, 0], {x, -
Infinity, Infinity}]
Out[54]=
1

In[55]:=
PiecewiseIntegrate[Piecewise[{{DiracDelta[x - 1/2], -1 < x < 1}}, 0],
{x, -Infinity, Infinity}]
Out[55]=
1

In the above mentioned notebook there many examples that demonstrates
PiecewiseIntegrate
capabilities.

Regards
Dimitris

=CF/=C7 Andrew Moylan =DD=E3=F1=E1=F8=E5:
> 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