Re: Integrating DiracDelta to get UnitStep

*To*: mathgroup at smc.vnet.net*Subject*: [mg91261] Re: Integrating DiracDelta to get UnitStep*From*: "David W.Cantrell" <DWCantrell at sigmaxi.net>*Date*: Tue, 12 Aug 2008 04:46:25 -0400 (EDT)*References*: <g7p2tm$arr$1@smc.vnet.net>

CRC <crobc at this-is-bogus.sbcglobal.net> wrote: > Hi: > > I am a bit confused by Mathematica 6.0.3 behavior. I expect that: > > In[n]:= Integrate[DiracDelta[x], {x, -\[Infinity], t}, > Assumptions -> Im[t] == 0] > > Will produce: > > Out[n]= UnitStep[t] > > But instead it produces: > > Out[n]= 1 > > However, > > In[n+1]:= Plot[ Integrate[DiracDelta[x], {x, -\[Infinity], t}, > Assumptions -> Im[t] == 0], {t, -2, 2} ] > > produces the expected plot of UnitStep[t]. > > Why doesn't the integration output the UnitStep function? I share your concern and will be interested to see what others say. Here's something which is closely related but which works as it should: In[2]:= Integrate[DiracDelta[x], {x, t, Infinity}, Assumptions -> Im[t] == 0] Out[2]= HeavisideTheta[-t] Perhaps that will help. David

**Follow-Ups**:**Re: Re: Integrating DiracDelta to get UnitStep***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>