Re: Can Mathematica NIntegrate a Log-type singularity?
- To: mathgroup at smc.vnet.net
- Subject: [mg92666] Re: [mg92642] Can Mathematica NIntegrate a Log-type singularity?
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Fri, 10 Oct 2008 04:32:50 -0400 (EDT)
- Reply-to: hanlonr at cox.net
$Version
6.0 for Mac OS X PowerPC (32-bit) (June 19, 2007)
nint = NIntegrate[alpha^2 * Log[2 Cos[alpha/2]]^2, {alpha, -Pi, Pi}]
37.4024
nint/Pi^5
0.122222
% // Rationalize
11/90
The result is stable for changes in WorkingPrecision. The integral appears to be 11/90 * Pi^5
Bob Hanlon
---- Aaron Fude <aaronfude at gmail.com> wrote:
=============
Hi,
I would like to evaluate the following:
NIntegrate[alpha^2 Log[2 Cos[alpha/2]]^2, { alpha, -Pi, Pi}]
How do I help Mathematica deal with the LogSquared type singularity at
either end of the interval. If I try it straight, Mathematica
complains and gives a wrong answer.
Please note, that Mathematica has absolutely no problem Integrating or
NIntegrating the function
Log[Cos[alpha/2]]^2
from -Pi to Pi, each time giving the correct answer, but the multiple
of alpha^2, throws it off.
Many thanks in advance,
Aaron.
PS: By the way, I'm pretty sure that that integral must be some
rational number times Pi^5.
--
Bob Hanlon