Riemannintegrálhatónak

Riemannintegrálhatónak is a Hungarian term that translates to "Riemann integrable" in English. It describes a property of a function that can be integrated using the Riemann integral. A function is Riemann integrable on a closed interval if the limit of its Riemann sums exists and is independent of the choice of sample points within each subinterval. This property is fundamental in calculus for defining the definite integral, which represents the signed area between the function's graph and the x-axis over a given interval. For a function to be Riemann integrable, it must be bounded on the interval and the set of its discontinuities must have Lebesgue measure zero. Continuous functions are always Riemann integrable, as are functions with a finite number of jump discontinuities. However, functions with more complex discontinuities, such as the Dirichlet function, are not Riemann integrable. The concept of Riemann integrability provides a rigorous framework for calculating areas and accumulating quantities.