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Re: Integrate vs NIntegrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89150] Re: Integrate vs NIntegrate
  • From: dh <dh at metrohm.ch>
  • Date: Tue, 27 May 2008 07:14:38 -0400 (EDT)
  • References: <g1e35c$er3$1@smc.vnet.net>


Hi Armen,

we cross a branch cut at x=2, as you may see by:

Plot[Re@f[x],{x,0,3}]

If you integrate from 0 to 2 and from 2+epsilon to 3, where epsilon is 

small enough for your purpose, you will get the same result from 

Integrate and NIntegrate.

hope this helps, Daniel



Armen Kocharyan wrote:

> Dear group,

> 

> 

> Why do I get different results (Res1, Res2) in Mathematica 6.0.1.0?

> 

> 

> *q=-1/2; a=0; b=3;*

> 

> *h[x_]=(1+x^3)^q;*

> 

> *f[x_]=Integrate[h[x],x];*

> 

> *Res1=N[f[b]-f[a]]*

> 

> *Res2=NIntegrate[h[x],{x,a,b}]*

> 

> **

> 

> *Res1 = -2.55387-2.42865 i*

> 

> *Res2 = 1.65267*

> 

> 

> 

> I'm assuming that Res2 is the correct answer.

> 

> 

> 

> Regards,

> 

> Armen

> 

> 





-- 



Daniel Huber

Metrohm Ltd.

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CH-9100 Herisau

Tel. +41 71 353 8585, Fax +41 71 353 8907

E-Mail:<mailto:dh at metrohm.com>

Internet:<http://www.metrohm.com>




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