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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, seeINTEGRAL and INTEGRAL CALCULUS.