Integral calculus - Integral - Calculation of functions

Formulas for calculation

The fundamental concepts and theories of integral and differential calculus, especially the relationship between differentiation and integration, and their application to the solution of applied problems. Their investigations were the beginning of an intensive development of mathematical analysis.

The works of L. Euler, Jacob and Johann Bernoulli and J. L. Lagrange played a major role in its development in the 18th

In the 19th century, integral calculus reached a logically complete form (in the works of A. L. Cauchy, B. Riemann and others) in connection with the emergence of the concept of the limit. The development of the theory and methods of integral calculus took place at the end of the 19th century and in the 20th century simultaneously with research into measure theory (cf. measurement), which plays an essential role in integral calculus.

With the help of integral calculus, many theoretical and applied problems could be solved in a unified way, both new ones that were previously unsolvable and old ones that previously required special artificial techniques. The basic concepts of integral calculus are two closely related notions of integral, namely the indefinite integral and the definite integral.

Calculating functions

The indefinite integral of a given function with real value in an interval on the real axis is defined as the collection of all primitives in this interval, i.e. functions whose derivatives are the given function. The indefinite integral of a function f is denoted by ∫ f (x) dx. If F is any basic element of f, every other basic element has the form F C, where C is an arbitrary constant