Integraalreeglite

Integraalreeglite, also known as the Fundamental Theorem of Calculus, is a cornerstone of calculus that establishes a relationship between differentiation and integration. It consists of two parts: the first part states that if a function f(x) is continuous on the closed interval [a, b], and F(x) is a function whose derivative is f(x) on [a, b], then the definite integral of f(x) from a to b is equal to F(b) - F(a). This part is often referred to as the evaluation theorem. The second part, known as the second fundamental theorem of calculus, states that if f(x) is continuous on [a, b], then the derivative of the integral of f(x) from a to x, with respect to x, is f(x). This theorem allows for the calculation of definite integrals by finding an antiderivative, which is a function whose derivative is the original function. The Fundamental Theorem of Calculus is crucial in various fields, including physics, engineering, and economics, as it provides a method to compute areas under curves and solve problems involving rates of change.