British Dictionary definitions for definite integral

definite integral

noun

1.

(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, ʃbaf(x)dx, where f(x) is the given function and x = a and x = b are the limits of integration. Where F(x) = ʃf(x)dx, the indefinite integral, ʃbaf(x)dx = F(b)–F(a)

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.