10.1.39 Integral of a complex variable
Condition: Calculate the integral over a function of a complex variable over a given curve: \[ \begin{array}{l} \int_{A B C} z \vec{z} d z ; \quad A B:\{|z|=1, \operatorname{Re} z \geq 0, \operatorname{lm} z \geq 0\} . \\ B C-\text { segment, } z_{B}=1, z_{c}=0 . \end{array}\]
Calculation of integrals from functions of a complex variable. Sub-integral functions can be either analytic or with singular points. Application of the main residue theorem, as well as the Cauchy formulas for calculating integrals of functions with poles in a simply connected domain.