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. Oberdorfstr. 68 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>