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

You should also know when it is best to use your calculator.​ It is typically most useful for graphing functions, computing numerical derivatives and definite integrals and solving equations.

From US News

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

From Project Gutenberg

But, as in the analogous cases of algebraic equations and definite integrals, it may be quite possible to find, by methods of approximation, an arithmetical solution which is sufficient for the purpose in hand.—Bibliography:

From Project Gutenberg

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 Project Gutenberg

All such definite integrals as the above are said to be “improper.”

From Project Gutenberg