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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 ba 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 ∫ 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.
- The result of an integration performed on a fixed interval.
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Word History and Origins
Origin of definite integral1
First recorded in 1875–80
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Example Sentences
The first inquiry leads directly to the indefinite integral, the second directly to the definite integral.
From Project Gutenberg
Integrators serve to evaluate a definite integral ∫ab f(x)dx.
From Project Gutenberg
While an integrator determines the value of a definite integral, hence a Integraphs.
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
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