integrálisintegrált

Integrálintegrált is a mathematical concept that refers to a function that has been integrated. In calculus, integration is the process of finding the antiderivative of a function. An antiderivative of a function f(x) is a function F(x) such that its derivative F'(x) is equal to f(x). The process of integration can be thought of as the reverse of differentiation.

When a function is integrated, the result is a new function that represents the accumulated area under the curve of the original function. This accumulated area can be interpreted in various ways depending on the context. For example, if the original function represents velocity, its integral represents the displacement or distance traveled. If the original function represents a rate of change, its integral represents the total change.

The indefinite integral of a function f(x) is denoted by $\int f(x) dx$ and results in a family of functions F(x) + C, where F(x) is a particular antiderivative and C is an arbitrary constant of integration. This constant arises because the derivative of any constant is zero, meaning there are infinitely many functions that have the same derivative. The definite integral, on the other hand, calculates the accumulated change of a function over a specific interval [a, b], denoted by $\int_a^b f(x) dx$. This evaluates to F(b) - F(a), giving a numerical value. Therefore, an integrálintegrált can refer to either the family of antiderivatives or the result of a definite integration.