Definite Integral

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The following article is from 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 It might be outdated or ideologically biased.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 Definite Integral. 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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
They should be familiar with the term "definite integral" and know how to find the antiderivative of a function.
LO 3.4A: Interpret the meaning of a definite integral within a problem.
As a pre-activity, students should be able to find the value of the definite integral [[integral].sup.6.sub.0] 2+2 sin(x)dx.
If a definite integral is desired, one must use the fact that
As the screen suggests, this particular device represents an indefinite integral by leaving blanks where the limits of a definite integral might appear.
Then the field is open to deal with anti-derivatives and solve simple differential equations, well before the definite integral is introduced through sequences of Riemann sums.
On the other hand, the following program allows students to approximate a definite integral between two points a and b: