The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves

In this paper is considered the extreme problem of searching for the optimal quadrature formulas in S. M. Nikolskiy sense for approximate calculation of curvilinear integrals of first kind on the class of differentiable functions, the second gradient norm of which in $L_P \ (1 \le p < \infty)$ is bounded along the curve by which the curvilinear integral is calculated. The exact errors of optimal quadrature formula for the studied class of functions were calculated, and the explicit formulas for optimal nodes and coefficients was shown.