Re: Bug in Calculus`DiracDelta`
- To: mathgroup at smc.vnet.net
- Subject: [mg14821] Re: Bug in Calculus`DiracDelta`
- From: "W. K. Bertram" <wkb at ansto.gov.au>
- Date: Wed, 18 Nov 1998 01:29:27 -0500
- Organization: Australian Nuclear Science and Technology Organisation
- References: <72je71$3f9@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
M. Rommel wrote:
> I know normally "it's the user, stupid!" but this one seems real.
>
> In[1]:= <<Calculus`DiracDelta`
>
> In[2]:= Integrate[DiracDelta[Cos[x]],{x,0,\[Pi]}]
>
> Out[2]= 1
>
> That's what I agree with but the next line I cannot:
>
> In[3]:= Integrate[DiracDelta[Cos[x]],{x,\[Pi],2\[Pi]}]
>
> Out[3]= 0
>
> Any comments/insights/etc. pp.?
>
Martin,
The second result is certainly wrong! I have always been told to be very
careful
with expressions containing delta functions. As a result I would always
transform
an integral such as the one above by making the argument of the delta
function the
variableof integration. Therefore, making the substitution,
u = Cos[x]
you would instead evaluate
Integrate[Sqrt[1-u^2] DiracDelta[u],{u, Cos[Pi], Cos[2Pi]}]
and this gives the correct result for all limits of integration.
Cheers,
Bill