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# definite integral

## noun

*Mathematics.*

- 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

- maths
- 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* - 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*)

definite integral

/ dĕf**′**ə-nĭt /

- The difference between the values of an indefinite integral evaluated at each of two limit points, usually expressed in the form
*ƒ(x)*between the limits and the*x*-axis if*f(x)*is greater than or equal to zero between the limits. - The result of an integration performed on a fixed interval.

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## Word History and Origins

Origin of definite integral^{1}

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## Compare Meanings

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

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## 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.

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