Mathematics generalizes applied problems by replacing physical, geometric quantities with abstract mathematical concepts (function, span or region of integration), investigates the conditions of integrability and offers practical recommendations for using a certain integral.
The need to use a certain integral leads to the task of calculating the area of the curvilinear region, the length of the arc, the volume and mass of a body with a variable density, the path traveled by a moving body, the work of a variable force, the electric field potential, and much more.Ĭommon to this type of problem is the approach to solving the problem: the large can be represented as the sum of the small, the area of the flat region can be represented as the sum of the areas of the rectangles into which the region is mentally divided, volume as the sum of the volumes of pieces, body weight as the sum of the masses of parts, etc. The concept of a specific integral and the calculation - integration procedure are found in a wide variety of problems in physics, chemistry, technology, mathematical biology, probability theory and mathematical statistics. The paper gives definitions of the basic concepts and formulations of theorems, working formulas and mathematical expressions, gives practical recommendations for the analysis of examples in order to facilitate the assimilation of the material and the implementation of the course calculation task. The teaching aid is intended for students of the biomedical faculty to assist in the development of educational material and the theoretical part of the educational material can be considered as a lecture notes.
#Calculus volume calculator manual
The manual is intended for undergraduate students studying the differential and integral calculus of the function of one variable in the framework of the curriculum. A large number of tasks for independent solutions are presented, including options for an individual calculation task containing situational (applied) tasks. Examples of solving typical problems are given. The manual contains the basics of the theory of a certain integral. Then function defined on the half-line and integrable on any interval The limit of the integral and is called the improper integral of the first kind of function a to and Improper integral is definite integral, which is unlimited or expanded function, or the region of integration, or both together Proper integral is a definite integral, which is bounded as expanded function, and the region of integration. An indefinite integral is the set of all antiderivatives some functionĪ definite integral of the function f (x) on the interval is the limit of integral sums when the diameter of the partitioning tends to zero if it exists independently of the partition and choice of points inside the elementary segments.
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