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Re: Integrate vs NIntegrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89151] Re: Integrate vs NIntegrate
  • From: dh <dh at metrohm.ch>
  • Date: Tue, 27 May 2008 07:14:49 -0400 (EDT)
  • References: <g1e35c$er3$1@smc.vnet.net>


Hi Armen,

the formula Inegrate[f[x],{x,a,b}]=F[a]-F[b], where F is the indefinite 

integral of f, is only valid if the integrand has no branch cuts. The 

reason is that F[x] has no knowledge about which path you want to take 

from a to b. One can therefore not count on F[a] and F[b] to lay on the 

same branch.

The remedy is not to use the indefinite integral, but to calculate the 

path integral. In your case the parametrization of the path is very 

simple because you can take x on the real axis as parameter:

Integrate[h[x],{x,a,b}]

hope this helps, Daniel



Armen Kocharyan wrote:

Thanks Daniel.



But why f[x] has a branch cut. I think it's artificial and Mathematica 

got it wrong.



Regards,

Armen





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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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