Study of the topic "Integral calculus" in the course of higher mathematics
The Article is devoted to one of the sections of mathematical analysis- integral calculus of the function of one and several variables. The article analyzes two approaches to the introduction of the concept of a certain integral. Some advantages and disadvantages of each method of administration are given. One of possible ways of generalization of a certain integral to curvilinear and surface integrals, and also multiple integrals is offered. The connection of curvilinear, surface and multiple integrals with a certain integral is shown, as well as the physical and mechanical meanings of different types of integral are indicated. Several examples of calculation of different types of integrals are given. The article also identifies the main errors and difficulties encountered in calculating the integrals of students, and offers some ways to prevent them.