integrálszámítás

Integrálszámítás is the Hungarian term for integral calculus, a fundamental branch of mathematics. It is concerned with the study of integrals, which can be interpreted geometrically as the area under a curve. Integrálszámítás is the inverse operation of differenciálás (differential calculus), a concept formalized by the Newton-Leibniz theorem. This theorem establishes the crucial link between differentiation and integration.

There are two main types of integrals: the indefinite integral and the definite integral. The indefinite integral, also known as an antiderivative, represents a family of functions whose derivative is a given function. The definite integral, on the other hand, calculates a specific numerical value, typically representing the net area between a function's graph and the x-axis over a given interval.

Integrálszámítás has widespread applications across various scientific and engineering disciplines. It is used to calculate volumes, surface areas, work done by a force, probabilities, and to solve differential equations that model real-world phenomena. Its development was a significant milestone in the history of mathematics, providing powerful tools for understanding and quantifying continuous change.