10.1.36 Integral of a complex variable
Condition: Calculate the integral of a function of a complex variable over a given curve: \[ \begin{array}{l} \int_{A B} z \operatorname{Im} z^{2}, \quad A B-\text { line segment, } \\ z_{A}=0, \quad z_{B}=1+i . \end{array}\]
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.