Integrating DircaDelta[x]
- To: mathgroup at smc.vnet.net
- Subject: [mg78443] Integrating DircaDelta[x]
- From: Pillsy <pillsbury at gmail.com>
- Date: Mon, 2 Jul 2007 06:43:28 -0400 (EDT)
In Mathematica 6, integrating the DiracDelta function with specified
limits gives the expected result:
In[1]:= Integrate[DiracDelta[x], {x, -Infinity, -1}]
Out[1]:= 0
In[2]:= Integrate[DiracDelta[x], {x, -Infinity, 1}]
Out[2]:= 1
In[3]:= Integrate[DiracDelta[x], {x, -Infinity, 0}]
Out[3]:= 1/2
But when you replace the limit with a variable, it returns something
quite different:
In[4]:= Integrate[DiracDelta[x], {x, -Infinity, a}]
Out[4]:= If[a \[Element] Reals, 1,
Integrate[DiracDelta[x], {x, -\[Infinity], a},
Assumptions -> Im[a] < 0 || Im[a] > 0]]
In[5]:= Map[% /. a -> # &, {-1, 0, 1}]
Out[5]:= {1, 1, 1}
Any idea what's going on? I'm using the 32-bit x86 Mac version on OS X
10.4.10, if it matters.
TIA,
Pillsy