# Thread: Evaluate the closed contour integral

1. ## Evaluate the closed contour integral

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

$\displaystyle$\int_\Gamma\bar{z}^3 dz$around the triangle$\displaystyle \Gamma$by suitably parametrizing the segments of the piecewise smooth contour$\displaystyle \Gamma$. Why doesn’t Cauchy’s theorem apply to this integral? 2. Originally Posted by lpd Consider a piecewise smooth contour$\displaystyle \Gamma$which is a triangle with vertices at$\displaystyle z = 0, 1 + i, i$. Evaluate the closed contour integral,$\displaystyle $\int_\Gamma\bar{z}^3 dz$

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

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

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

Tonio