MathProblemsBank

10.1.38 Integral of a complex variable

Condition: Using the Cauchy integral formula and its generalizations, calculate the integral: \[ \oint_{|z|=\frac{1}{3}} \frac{e^{2}-\sin z}{z^{2}} d z . \]

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.

-> Integral of a complex variable