Fundamental theorem of calculus
Main article: Fundamental theorem of calculus The fundamental theorem of calculus specifies the relationship between the two central operations of calculus: differentiation and integrationThe fundamental theorem of calculus is the statement that differentiation In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point. For example, the derivative of the position of a vehicle with respect to time is the instantaneous velocity (respectively, and integration are inverse operations: if a continuous function In mathematics, a continuous function is a function for which, intuitively, small changes in the input result in small changes in the output. Otherwise, a function is said to be discontinuous. A continuous function with a continuous inverse function is called bicontinuous. An intuitive though imprecise idea of continuity is given by the common is first integrated and then differentiated, the original function is retrieved. An important consequence, sometimes called the second fundamental theorem of calculus, allows one to compute integrals by using an antiderivative In calculus, an antiderivative, primitive or indefinite integral of a function f is a function F whose derivative is equal to f, i.e., F ′ = f. The process of solving for antiderivatives is antidifferentiation . Antiderivatives are related to definite integrals through the fundamental theorem of calculus: the definite integral of a function over of the function to be integrated.
<<Table of Contents Integration is an important concept in mathematics which, together with differentiation, forms one of the main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of the real line, the definite integral | Next>> | Show All>>
