# Definite Integral

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## 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, seeINTEGRAL and INTEGRAL CALCULUS.

References in periodicals archive ?
Obviously, this is an 8-fold definite integral which could be computed with the proposed number theory based numerical integration.
Still, Steele's definite integrals have some merit as tools for expositing Hayek's pure theory of capital: they recognize and give play to the notion that capital must be measured in two dimensions (value and time) and that changes in market conditions may have different effects on different components of the capital structure.
equals p.sub.4 / [the definite integral from negative infinity to infinity of] (f.sub.B of ([the integer portion of] x + 0.5) dx / f.sub.B of(M)
After this, we presented deductions that allowed us to represent it by using mathematics, initially utilizing the concept of the definite integral and then with the application of Green's theorem as a language for the modeling of its functioning, thus demonstrating the effectiveness of the instrument and its accuracy in the measurement of areas on different regions.
Let (x, t) [member of] [OMEGA] x [[t.sub.1], [infinity]) on the x be the definite integral in [OMEGA].
After the engine is implemented, a definite integral process is used as an example.
Thus it is equal to the definite integral [[integral].sup.b.sub.0] 1 + 1 + x dx, which can be calculated by elementary calculus (see [3] and [4]):
As can be seen, the numerical integration methods are able to approximate a value for a definite integral using the values of the function at points within the interval of the integrand.
Generally, the primitive of a Lagrange 1-form L(t,x(t),[??](t))dt can be written either as (definite integral)
Multipy [T.sub.m](x)/[square root of([1 - [chi square]] (m = 0, 1, ...) to the two sides of (1) and definite integral from--1 to 1.

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