Re: Incorrect symbolic improper integral
- To: mathgroup at smc.vnet.net
- Subject: [mg103605] Re: [mg103586] Incorrect symbolic improper integral
- From: Mark McClure <mcmcclur at unca.edu>
- Date: Wed, 30 Sep 2009 04:59:13 -0400 (EDT)
- References: <200909291138.HAA25632@smc.vnet.net>
On Tue, Sep 29, 2009 at 7:38 AM, jwmerrill at gmail.com
<jwmerrill at gmail.com> wrote:
> Below is a definite integral that Mathematica does incorrectly.
> In[62]:= Integrate[Cos[x]/(1 + x^2), {x, -\[Infinity], \[Infinity]}]
> Out[62]= \[Pi]/E
>
> What a pretty result--if it were true. The correct answer is \[Pi]*Cosh
> [1], which can be checked by adding a new parameter inside the
> argument of Cos and setting it to 1 at the end:
>
> In[61]:= Integrate[Cos[a x]/(1 + x^2), {x, -\[Infinity], \[Infinity]},
> Assumptions -> a \[Element] Reals]
> Out[61]= \[Pi] Cosh[a]
The Pi/E result is correct, as can be computed using residue theory.
While not fullproof, it's also generally a good idea to compare these
types of results against NIntegrate.
Of course, the result with the parameter must be incorrect.
Are you using V7.0.0? A bug with this type of integral was
introduced in V7.0.0 but fixed by V7.0.1.
Mark McClure
- References:
- Incorrect symbolic improper integral
- From: "jwmerrill@gmail.com" <jwmerrill@gmail.com>
- Incorrect symbolic improper integral