Re: Improper integral

• To: mathgroup at smc.vnet.net
• Subject: [mg44621] Re: Improper integral
• From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
• Date: Tue, 18 Nov 2003 06:41:51 -0500 (EST)
• References: <bpa2sm\$1eh\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```poujadej at yahoo.fr (Jean-Claude Poujade) wrote:
> Bonjour le groupe,
>
> I'm not a mathematician and I wonder why Mathematica doesn't return 0
> for this doubly infinite improper integral :
>
> In[1]:=\$Version
> Out[1]=4.1 for Microsoft Windows (November 2, 2000)
>
> In[2]:=Integrate[x/(1+x^2),{x,-Infinity,Infinity},PrincipalValue->True]
> Integrate::idiv[...]does not converge[...]
> Out[2]:=Integrate[x/(1+x^2),{x,-Infinity,Infinity},PrincipalValue->True]
>
> maybe it's different with Mathematica 5.0 ?

Unfortunately, version 5 does the same thing.

Here's what you can do to help Mathematica get the principal value:

Limit[Integrate[x/(1+x^2),{x,-a,0}]+Integrate[x/(1+x^2),{x,0,a}],a->Infinity]

That returns 0, as it should.

David

```

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