       Re: DiracDelta Function question

• To: mathgroup at smc.vnet.net
• Subject: [mg21141] Re: DiracDelta Function question
• From: Bojan Bistrovic <bojanb at physics.odu.edu>
• Date: Fri, 17 Dec 1999 01:21:42 -0500 (EST)
• Organization: Old Dominion Universityaruba
• References: <831vk0\$g89@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Julian Francis wrote:
>
> Folks,
>
> Why is mathematica unable to evaluate:
> Integrate[DiracDelta[2 x - 1], {x, -Infinity, +Infinity}]
>
> Also interestingly:
> Integrate[DiracDelta[2 x - 2], {x, -Infinity, +Infinity}]
>
> returns (1/2)
>
> I should have thought that the answer in both cases would be 1.
>
> I am using Mathematica v4.0 on MS Windows 95.
>
> Thanks for any light shed on this.
>
> Julian Francis.
> acz43 at dial.pipex.com

It's probably a bug in MS-Windows :-). My Linux version returns 1/2 in
both cases which is correct. There's a general formula for Dirac
function: if f[x] is a function with a FIRST ORDER zero f[x_0]=0, then

DiracDelta[f[x]] =  DiracDelta[x-x_0]/Abs[f'[x_0]]

If there's more than one zero in the integration range, one should sum
over all zeroes. In this case, x_0 equals 1/2 and 1, and f'[x_0] ewuals
2 in both cases, so the result is 1/2.

-------------------------------------------------------------
Bojan Bistrovic,                       bojanb at physics.odu.edu
Old Dominion University, Physics Department,      Norfolk, VA
-------------------------------------------------------------

```

• Prev by Date: Re: question
• Next by Date: Re: A Bitmap file as input for Mathematica 3.0
• Previous by thread: Re: DiracDelta Function question
• Next by thread: Re: DiracDelta Function question