(Igor Sikorsky Kyiv Polytechnic Institute, 2019) Zhuravska, Ganna V.
This textbook is designed for students of the first year of technical university. It covers content area to be studied in the first and second semesters: Integral Calculus of a Function of One Variable.
It is concerned with the concept of indefinite, definite and improper integrals, their properties and main techniques of integration. Also we take a look at some applications of integrals: determining area of a region, the arc length of a curve, the surface area and the volume of a solid of revolution, the center of mass and moments of inertia of a region and curve.
Each part contains basic mathematical conceptions and explains new mathematical terms. The most important concepts of Integral Calculus are explained and illustrated by figures and examples. The manual contains theoretical material, which presents the basic formulas, definitions and theorems, illustrated by examples and figures, shows the basic methods of solving typical problems.
The proposed manual will help students of engineering specialties studying the Integral Calculus of a Function of One Variable.