# [SOLVED] Complex integral

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• Sep 16th 2009, 09:30 AM
arbolis
[SOLVED] Complex integral
I must calculate $\int _1^3 (z-2)^3 dz$ where the path is an arbitrary contour between the limits of integration.

I simply calculated the integral as if $z$ was a real variable in order to get that it's worth $0$.
Am I right?
• Sep 16th 2009, 11:33 AM
shawsend
You can use antiderivatives because the integrand is analytic and single-valued over the contour.
• Sep 16th 2009, 11:36 AM
Opalg
Quote:

Originally Posted by arbolis
I must calculate $\int _1^3 (z-2)^3 dz$ where the path is an arbitrary contour between the limits of integration.

I simply calculated the integral as if $z$ was a real variable in order to get that it's worth $0$.
Am I right?

Yes. The function has an indefinite integral, so all you need to do is to evaluate that at the two ends of the path.