definite integral


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definite integral

n.
1. An integral that is calculated between two specified limits, usually expressed in the form b/a ƒ(x)dx. The result of performing the integral is a number that represents the area under the curve of ƒ(x) between the limits and the x-axis if f(x) is greater than or equal to zero between the limits.
2. The result of an integration performed on a fixed interval.

definite integral

n
(Mathematics) maths
a. the evaluation of the indefinite integral between two limits, representing the area between the given function and the x-axis between these two values of x
b. the expression for that function, ∫baf(x)dx, where f(x) is the given function and x = a and x = b are the limits of integration. Where F(x) = ∫f(x)dx, the indefinite integral, ∫baf(x)dx = F(b)–F(a)

def′inite in′tegral


n.
the representation, usu. in symbolic form, of the difference in values of a primitive of a given function evaluated at two designated points. Compare indefinite integral.
[1875–80]
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.definite integral - the integral of a function over a definite intervaldefinite integral - the integral of a function over a definite interval
integral - the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)
Translations
određeni integral
定積分
References in periodicals archive ?
While it is a good practice after obtaining a definite integral to find its derivative as a check that the manipulations were carried out correctly, and a nice reminder of the relationship between the functions concerned, this can sometimes be tedious and at other times can be extremely tedious, so is frequently not done by time-poor or symbolic manipulation-averse students.
After the topic on the area of plane regions has been discussed, a second instrument was given to measure their understanding of the area concept as a geometric application of the definite integral.
Similarly int(S v a b) is the definite integral of S with respect to v from a to b.
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.
Let A'(v) and F'(s) denote a new integral transform and the Laplace transform of the definite integral of f(t).
Taking their sum and the definite integral for any closed interval [a,b] yields
The steps of the Chaotic Harmony Search algorithm for calculating numerical value of definite Integral (CHSINT) are as follows:
It is well-known that for single-fold definite integral, Gauss quadrature may serve as an accurate numerical approximation in most cases [11].
Nine studies consider representing and defining irrational numbers, student use of Derive software in comprehending and making sense of definite integral and area concepts, perspectives by mathematicians on teaching and learning proof, case studies from a transition-to-proof course on referential and syntactic approaches to proving, infinite iterative processes and actual infinity, teaching assistants learning how students think, the knowledge base about teaching among teachers of calculus in higher education, modeling students' conceptions, and strategies for controlling the work in mathematics textbooks for introductory calculus.
There are several rules for the approximate evaluation of real definite integral