Toronto Math Forum
MAT3342018F => MAT334Tests => Quiz4 => Topic started by: Victor Ivrii on October 26, 2018, 05:48:15 PM

Evaluate the given integral using Cauchy’s Formula or Theorem. Orientation counterclockwise:
$$
\int_{z=1} \frac{z\,dz} {(z2)^2}.
$$

\begin{equation*}
This\ formula\ cannot\ be\ rewritten\ with\ Cauchy's\ formula,\ so\ we\ use\ Cauchy's\ theorem.\\
\\
\int _{z\ =\ 1} f( z) dz\ =\ 0\\
\\
\int _{z\ =\ 1} \ \frac{z}{( z2)^{2}} \ dz\ =\ 0\\
\end{equation*}