A First Course in Complex Analysis · Problem 37

Consequences of Cauchy's Theorem — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · cauchys-integral-formula

Problem

Compute the following integrals. (a)

\displaystyle\int_{C[-1,2]} \frac{z^2}{4 - z^2}\, dz

(b)

\displaystyle\int_{C[0,1]} \frac{\sin z}{z}\, dz

(c)

\displaystyle\int_{C[0,2]} \frac{\exp(z)}{z(z-3)}\, dz

(d)

\displaystyle\int_{C[0,4]} \frac{\exp(z)}{z(z-3)}\, dz