# Thread: Evaluate the closed contour integral

1. ## Evaluate the closed contour integral

Consider a piecewise smooth contour $\Gamma$ which is a triangle with vertices at $z = 0, 1 + i, i$. Evaluate the closed contour integral,

$\int_\Gamma\bar{z}^3 dz$

around the triangle $\Gamma$ by suitably parametrizing the segments of the piecewise smooth contour $\Gamma$.

Why doesn’t Cauchy’s theorem apply to this integral?

2. Originally Posted by lpd
Consider a piecewise smooth contour $\Gamma$ which is a triangle with vertices at $z = 0, 1 + i, i$. Evaluate the closed contour integral,

$\int_\Gamma\bar{z}^3 dz$

around the triangle $\Gamma$ by suitably parametrizing the segments of the piecewise smooth contour $\Gamma$.

Why doesn’t Cauchy’s theorem apply to this integral?

Because $f(z)=\bar{z}^3$ isn't analytic...

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