Re: Integrating DircaDelta[x]
- To: mathgroup at smc.vnet.net
- Subject: [mg78536] Re: Integrating DircaDelta[x]
- From: dh <dh at metrohm.ch>
- Date: Tue, 3 Jul 2007 06:51:28 -0400 (EDT)
Hi Phillys,
I think we simply have a bug here. Wolfram should take note. Consider:
Integrate[DiracDelta[x],{x,-Infinity,a},Assumptions->{Element[a,Reals]}]
gives 1, however if we add a<0 to the assumptions:
Integrate[DiracDelta[x],{x,-Infinity,a},Assumptions->{Element[a,Reals],a<0}]
we get 0.
Daniel
Pillsy wrote:
> 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
>
>