definite integral

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.

definite integral

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 ^ba f ( x ) dx = F ( b ) –F ( a )

definite integral

/ 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.

Word History and Origins

Origin of definite integral¹

First recorded in 1875–80

Example Sentences

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 Project Gutenberg

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

From Project Gutenberg

When the improper definite integral of a function which becomes, or tends to become, infinite, exists, the integral is said to be “convergent.”

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

The instrument now is an integraph giving the value of a definite integral as function of a variable parameter.

From Project Gutenberg