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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How does definite-integral compare to similar and commonly confused words? Explore the most common comparisons:

• definite integral vs. indefinite integral

Example Sentences

In this section, we look at how to apply the concept of the area under the curve to a broader set of functions through the use of the definite integral.

From Textbooks • Mar. 30, 2016

Figure 1.28 The evaluation of a definite integral can produce a negative value, even though area is always positive.

From Textbooks • Mar. 30, 2016

In addition, a careful examination of Figure 3.15 leads us to make the following observations about using the trapezoidal rules and midpoint rules to estimate the definite integral of a nonnegative function.

From Textbooks • Mar. 30, 2016

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

From Textbooks • Mar. 30, 2016

The representation of a function by means of an infinite product falls clearly under Baire’s method, while the representation by means of a definite integral is analogous to Brod�n’s method.

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