# 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

/ dĕfə-nĭt /

1. The difference between the values of an indefinite integral evaluated at each of two limit points, usually expressed in the form 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

## Compare Meanings

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

## Example Sentences

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

Integrators serve to evaluate a definite integral ∫ab f(x)dx.

While an integrator determines the value of a definite integral, hence a Integraphs.

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

## Word of the Day

petrichor

[pet-ri-kawr]

Meaning and examples

Start each day with the Word of the Day in your inbox!

By clicking "Sign Up", you are accepting Dictionary.com Terms & Conditions and Privacy Policies.