Re: A wrong definite integral in 5.0?

*To*: mathgroup at smc.vnet.net*Subject*: [mg77229] Re: A wrong definite integral in 5.0?*From*: Valeri Astanoff <astanoff at gmail.com>*Date*: Wed, 6 Jun 2007 06:45:12 -0400 (EDT)*References*: <f43hau$301$1@smc.vnet.net>

On 5 juin, 13:27, bolud-el-kotur <ke8e... at hotmail.com> wrote: > I get this result in version 5.0, > > >Integrate[Log[1 - 4 x(1 - x)], {x, 0, 1}] > >-2 + I Pi > > and the same thing if I "declare" the singularity with {x,0,1/2,1}. > > Another way to look at the problem is computing, > > >Integrate[Log[1 - 4 x(1 - x)], {x, 0, 1/2}] > >-1 > > and > > >Integrate[Log[1 - 4 x(1 - x)], {x, 1/2, 1}] > >-1 + I Pi > > Since the integrand is symmetric about x=1/2, the result should have > been the same one (-1) in both cases, and the integral over [0,1] > should yield -2. > > A numerical approach, > > >NIntegrate[Log[1 - 4 x(1 - x)], {x, 0, 1/2, 1}, > > MaxRecursion -> 100, SingularityDepth -> 20] > > >-1.9999997086422834` > > gives the correct result, within the numerical accuracy required. Good day, It was corrected in version 5.1 : In[1]:= Integrate[Log[1-4 x(1-x)],{x,0,1}] Out[1]=-2 In[2]:=$Version Out[2]=5.1 for Microsoft Windows (January 28, 2005) V.Astanoff