Complex Analysis: Theory and Applications · Problem 6.3.5

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · cauchy-goursat-theorem

Problem

Find

\displaystyle\int_C (2z-1)(z^2-z)^{-1}\,dz

for the following: (a) The circle

C = C_2^+(0) = \{z : |z| = 2\}

having positive orientation. (b) The circle

C = C_{\frac{1}{2}}^+(0) = \{z : |z| = \frac{1}{2}\}

having positive orientation.