Primitivfunktionen

Primitivfunktionen, also known as antiderivatives, are a fundamental concept in calculus. A function F is considered a primitivfunktion of another function f if the derivative of F is equal to f. In simpler terms, if you differentiate F, you get f back. The process of finding a primitivfunktion is called antidifferentiation or integration. Every continuous function has a primitivfunktion.

The relationship between a function and its primitivfunktion is not unique. If F is a primitivfunktion of f, then any function of the form F(x) + C, where C is an arbitrary constant, is also a primitivfunktion of f. This is because the derivative of a constant is always zero, so differentiating F(x) + C results in F'(x) + 0, which is still f(x). This constant C is often referred to as the constant of integration.

When seeking a specific primitivfunktion, additional information, such as a point the function must pass through, is required to determine the value of C. The indefinite integral, denoted by the integral symbol ∫, represents the family of all primitivfunktionen of a given function. For instance, the indefinite integral of 2x is x² + C, encompassing all possible primitivfunktionen of 2x.