10.1.31 Integral of a complex variable

Problem: Calculate the integral of the complex variable: \[ \int_{L} f(z) d z \text {, where } f(z)=z \bar{z} \text {; } \] \( L \) : the contour of the circular segment with the \( \operatorname{arc} z=e^{i t}, 0 \leq t \leq \pi / 2 \).