FEATURES OF THE USE OF INTEGRALS FOR SOLVING PROBLEMS WITH PHYSICOCHEMICAL CONTENT

The article considers some examples of application of integrals, which can be used in practical classes in higher mathematics, teaching students of chemical specialities. Examples of problems with physical and chemical content are given. Most often, when studying the course of higher mathematics it is necessary to solve problems of general character. But for the students of the Training and Research Institute of Chemical Technologies and Engineering the tasks that are directly related to their speciality are of greater interest. Thus, by considering the tasks such as those given in this article, we will increase the interest and motivation of future specialists to study this material. Also, when applying complex training sessions, students form and develop professional competences that allow them to perform engineering research work on specific technological processes. When solving many problems of both applied and theoretical nature it is necessary to sum up an infinite number of infinitesimal summands. This operation leads to one of the central concepts of mathematical analysis - the concept of integral (or definite integral). The definite integral is widely used in numerous applied mathematical and physical problems. For example, the application of the definite integral in geometric problems shows itself when solving problems to find areas of plane figures and surfaces that have complex shapes. The definite integral is applicable for finding the volume of a body of rotation, a body of arbitrary shape, as well as for finding the length of a curve, both in the plane and in space. The definite integral is used to calculate statistical moments, masses and centres of masses for arbitrary curves and surfaces in physics and theoretical mechanics problems. It can also be applied in calculating the work of force along a given path and other problems.