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Re: Integrate vs. NIntegrate


carlos at colorado.edu (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.

The second one is correct (except for the last few decimal places).

What version are you using? In version 5.0.0.0,

f = 2 + Cos[2*x] + I*Sin[2*x];
Simplify[Integrate[Log[f], {x, -Pi, Pi}]/(2*Pi)]

  Log[2]

N[%]

  0.6931471805599453

David Cantrell


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