Primitivfunktsioon

Primitivfunktsioon, also known as an antiderivative, is a fundamental concept in calculus. Given a function f(x), a primitivfunktsioon F(x) is a function whose derivative is f(x). In other words, if F'(x) = f(x), then F(x) is a primitivfunktsioon of f(x).

The process of finding a primitivfunktsioon is called antidifferentiation or integration. For any given function f(x), there are infinitely many primitivfunktsioon. These primitivfunktsioon differ only by a constant value. If F(x) is a primitivfunktsioon of f(x), then F(x) + C, where C is any constant, is also a primitivfunktsioon of f(x). This is because the derivative of a constant is always zero, so (F(x) + C)' = F'(x) + 0 = f(x).

The set of all primitivfunktsioon of a function f(x) is denoted by the indefinite integral, written as ∫f(x) dx = F(x) + C. The indefinite integral represents the general form of the primitivfunktsioon.

Primitivfunktsioon have numerous applications in mathematics and science. They are crucial for solving differential equations, calculating areas under curves, finding volumes of solids, and in various physics and engineering problems. For example, if you know the velocity of an object as a function of time, you can find its position by finding the primitivfunktsioon of the velocity function.