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MathGroup Archive 1998

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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



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