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Re: Integral of Piecewise function involving DiracDelta

• To: mathgroup at smc.vnet.net
• Subject: [mg74798] Re: Integral of Piecewise function involving DiracDelta
• From: "Michael Weyrauch" <michael.weyrauch at gmx.de>
• Date: Thu, 5 Apr 2007 04:16:27 -0400 (EDT)
• References: <euvmuo$epv$1@smc.vnet.net>

Hello,

   well in answering this question one could quote the documentation, which under "Numerical Functions"
says that "Piecewise represents piecewise functions". And DiracDelta is not a function. 

So for me Piecewise and DiracDelta don't go together mathematically well. I would suggest
to put the different integration intervals into the integration limits and NOT use Piecewise
together with a distribution like DiracDelta. Thats also mathematically more sensible, I believe.

Maybe Mathematica should rather issue a warning like "Don't do things like that" rather that returning a questionable
result.

Regards,   Michael Weyrauch


"Andrew Moylan" <andrew.j.moylan at gmail.com> schrieb im Newsbeitrag news:euvmuo$epv$1 at smc.vnet.net...
> 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
> 
>