# Definite Integral

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*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.## Definite Integral

one of the fundamental concepts of mathematical analysis; the solution of a number of problems in geometry, mechanics, and physics reduces to a definite integral. The definite integral is a number equal to the limit of the sums of a particular type (integral sums) corresponding to a function *f(x*) and an interval [*a, b*]; it is denoted by . Geometrically, the definite integral expresses the area of a “curvilinear trapezoid” bounded by the interval [*a, b*] on the *x*-axis, the graph of the function *f(x*), and the ordinates of the points on the graph that have abscissas *a* and *b.* For a precise definition and generalization of the definite integral, *see*INTEGRAL and INTEGRAL CALCULUS.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.