Ορισμένο Ολοκλήρωμα

Abstract

Ορισμός, ιδιότητες, θεωρήματα μέσης τιμής, υπολογισμός, γενικευμένα ολοκληρώματα, εφαρμογές

The original idea of the definite integral as an approximation of the area of a geometric figure is first encountered in antiquity in the 3rd BC century with Archimedes, who used approximate methods to calculate the area of the circle, helix, etc. In the middle of the 18th century, Riemann defined it in pure mathematical terms. That definition was then generalized by a number of other scientists, but its most important generalization was made by Lebesgue at the beginning of the 19th century. The definite integrals, in addition to the calculation of areas, are also used in many other applications that cover the whole of the positive sciences, some of which will be given in the following lesson.