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Q: Contour integral

Hi folks,

I have the following question:  I've been reading "Mathematica for
scientists and engineers", and there is an example on how to calculate
numerically a contour integral:


When applying this to a limacon:

NContourIntegrate[1/(z-1/2),z->Exp[I t](2Cos[t]+1),{t,0,2 Pi}]

one gets the right answer:

\!\(3.33066907387546962`*^-16 + 12.5663706143520892`\ I\)

(4pi I)

However, when modifying the numerical integration into an analytic one,

The answer that is obtained is wrong:

2 Pi I

Any ideas ?


PS: Please, also reply by mail...

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