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