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Integrating DiracDelta to get UnitStep

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  • Subject: [mg91238] Integrating DiracDelta to get UnitStep
  • From: CRC <crobc at>
  • Date: Mon, 11 Aug 2008 06:05:32 -0400 (EDT)


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


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?

Thanks for input.

crobc at
SuSE 10.3 Linux

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