definite integral

American  

noun

Mathematics.

1. the representation, usually in symbolic form, of the difference in values of a primitive of a given function evaluated at two designated points.

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definite integral British  

noun

1. maths

   1. 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

   2. the expression for that function, ʃ baf ( x ) dx , where f ( x ) is the given function and x = a and x = b are the limits of integration. Where F ( x ) = ʃ f ( x ) dx , the indefinite integral, ʃ ^b a f ( x ) dx = F ( b ) –F ( a )

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definite integral Scientific  

/ dĕf′ə-nĭt /

1. The difference between the values of an indefinite integral evaluated at each of two limit points, usually expressed in the form ∫ b/a ƒ(x)dx. The result of performing the integral is a number that represents the area bounded by 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.

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Etymology

Origin of definite integral

First recorded in 1875–80

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• definite integral vs. indefinite integral

Example Sentences

See Examples For:

definite integral

Simpson’s rule approximates the definite integral by first approximating the original function using piecewise quadratic functions.

From Textbooks ● Mar. 30, 2016

Use the definition of the definite integral to evaluate ∫ 2x2 dx.

From Textbooks ● Mar. 30, 2016

Figure 3.14 Trapezoids may be used to approximate the area under a curve, hence approximating the definite integral.

From Textbooks ● Mar. 30, 2016

In the following exercises, use a change of variables to evaluate the definite integral.

From Textbooks ● Mar. 30, 2016

While an integrator determines the value of a definite integral, hence a Integraphs. mere constant, an integraph gives the value of an indefinite integral, which is a function of x.

From Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" by Various