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MathGroup Archive 2004

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Re: Integrate vs. NIntegrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51426] Re: [mg51419] Integrate vs. NIntegrate
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sun, 17 Oct 2004 03:05:12 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

This appears to be version dependent.

$Version

5.0 for Mac OS X (November 19, 2003)

f=2+Cos[2 x]+I*Sin[2 x];

N[Integrate[Log[f],{x,-Pi,Pi}]/(2*Pi)]//InputForm

0.6931471805599453

NIntegrate[Log[f],{x,-Pi,Pi}]/(2*Pi)//InputForm

0.693147180559943 + 0.*I


Bob Hanlon

> 
> From: carlos at colorado.edu (Carlos Felippa)
To: mathgroup at smc.vnet.net
> Date: 2004/10/16 Sat AM 04:21:20 EDT
> To: mathgroup at smc.vnet.net
> Subject: [mg51426] [mg51419] Integrate vs. NIntegrate
> 
> 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.
> 
> 


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