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

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, compute each definite integral.

From Textbooks ● Mar. 30, 2016

On the other hand, the midpoint rule tends to average out these errors somewhat by partially overestimating and partially underestimating the value of the definite integral over these same types of intervals.

From Textbooks ● Mar. 30, 2016

The first inquiry leads directly to the indefinite integral, the second directly to the definite integral.

From Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3 "Frost" to "Fyzabad" by Various