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 > >