Re: A wrong definite integral in 5.0?

*To*: mathgroup at smc.vnet.net*Subject*: [mg77319] Re: A wrong definite integral in 5.0?*From*: dh <dh at metrohm.ch>*Date*: Wed, 6 Jun 2007 07:32:06 -0400 (EDT)*References*: <f43hau$301$1@smc.vnet.net>

Hi, you will remember from calculus that Log is a multivalued function: principal value + 2Pi n I. Therefore, the results are correct (but not as consistent as you would like it). Hint: in version 6 you get -1 for both integrals. hope this help, Daniel bolud-el-kotur 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. > >