The object of study is a numerical integration of the functions of several variables using new information operators. The cubature formulas of the approximate calculation of double and triple integrals for different information operators are presented. Information about function is given not only by the values of a function in nodes, but also as a set of traces of a function on planes or as a set of traces of a function on lines. Attention is paid to the application of such approximate calculation of integrals in various fields of science.

The development of information technology contributes to the improvement of mathematical models of phenomena and processes in many scientific areas of the technical direction. In particular, modern methods of digital signal and image processing use algorithms with new information operators. Cubature formulas are constructed for the approximate calculation of integrals of highly oscillating functions of many variables for various types of data. The paper deals with the estimation of the error in the numerical integration of highly oscillating functions of a general form on the class of differentiable functions of three variables in the case when information about the functions is given to their traces on the corresponding planes. The results obtained make it possible to research the quality of cubature formulas for the approximate calculation of triple integrals of highly oscillating functions of a general form.