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Re: Integrate vs. NIntegrate

  • To: mathgroup at
  • Subject: [mg51422] Re: Integrate vs. NIntegrate
  • From: Peter Pein <petsie at>
  • Date: Sun, 17 Oct 2004 03:05:06 -0400 (EDT)
  • References: <ckqnbf$nh0$>
  • Sender: owner-wri-mathgroup at

Carlos Felippa wrote:
> Which one is the correct answer?
> f=2+Cos[2 x]+ I*Sin[2 x];
> Print[ N[Simplify[ Integrate[Log[f],{x,-Pi,Pi}]/(2*Pi)]] //InputForm];
> 0.34657359027997264 + 1.5707963267948966*I
> Print[            NIntegrate[Log[f],{x,-Pi,Pi}]/(2*Pi)   //InputForm];
> 0.6931471805599428 + 0.*I
> I believe the second one, have doubts about the first.
since you integrate twice along the unit circle with center 2 and 
log(conj(z))==conj(log(z)) on this path, the imaginary part has to 
cancel out. (or I'm wrong?)

You can easily verify it:
Integrate[Log[2 + Exp[2*I*x]], {x, -Pi, Pi}]/(2*Pi)


Peter Pein, Berlin

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