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