Author: Хуррамов, Ёдгор Сафарали ўғли

Annotation: In many areas of mathematics, problems related to integrals of functions of several variables are encountered, and the importance of studying the calculation and application of multiple integrals is obvious. In the theory of multiple integrals, as in the theory of definite integrals, there are such concepts as the existence of an integral, its properties, calculation of an integral, and application of an integral. It should be noted that if in definite integrals the integration interval consists of segments in the P-space, then multiple integrals are integrated over regions of the corresponding space. The diversity of such regions complicates the study of multiple integrals and leads to differentiation of multiple integrals. The simplest of multiple integrals is the double integral. In this paper, applied aspects of double integrals are investigated. It is known that the problem of the area of ​​a curvilinear trapezoid leads to a simple definite integral. In the same way, the problem of the surface area and volume of a cylindrical body can be calculated using a double integral over a region. This article provides an idea of ​​how to calculate geometric and mechanical problems using double integrals. The paper presents concepts that contribute to the enrichment of mathematical knowledge of young engineers educated in the polytechnic field, as well as to the improvement of their professional knowledge and skills in their specialization. The formation of a student's mathematical competence is important from the point of view of the sufficiency of mathematical knowledge for calculating various types of surfaces, determining the volume and density of objects. Formulas for calculating the volume of a complex-shaped object are given.

Keywords: engineering specialty, mathematical competence, double integral, domain of integration, order of integration, mechanical, geometric interpretation.

Pages in journal: 85 - 95