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
--
Daniel Huber
Metrohm Ltd.
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CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
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