(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

where C is the contour given with direction marked by increasing y, and where -2≤y≤2 , compute itgeral(z^2-2z+1)dz. With the condition x=5;

Firstly I solved the auestion with the classical way ;

taking z= 5 + it where -2≤t≤2;

we take the i*integral((5+it)^2-2(5+it) +1)dt from t=-2 to t=2 and I found the result as

176i/3.

Then I tried to use the path independence theorem. The antiderivative of z^2-2z+1 is z^3/3 - z^2 + z then taking the integral from 2i to -2i yields -4i/3. So the two answers are different. Why the path independence theorem did not work here?[/QUOTE]

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# Homework Help: Why the path independence theorem does not work?

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