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Fundamental concept of calculus related to areas and other quantities modeled by functions. A definite integral gives the area between the graph of a function and the horizontal axis between vertical lines at the endpoints of an interval. It also calculates the net change in a system over an interval, thus leading to formulas for the work done by a varying force or the distance traveled by an object moving at varying speeds. When only the function is given, with no interval, it is known as an indefinite integral. The process of solving either a definite or an indefinite integral is called integration. According to the fundamental theorem of calculus, a definite integral can be calculated by using its antiderivative (a function whose rate of change, or derivative, equals the function being integrated). Integrals extend to higher dimensions through multiple integrals. See alsoline integral; surface integral.
This entry comes from Encyclopædia Britannica Concise. For the full entry on integral, visit Britannica.com.