The theorem that equates the definite integral of a function to the product of the interval over which the function is integrated and the value of the fuction at a point within the interval.

The theorem states that if the function f(x) is continuous on the interval [a b], then there exists at least one number ξ, in [a b] that satisfies the following equation:

∫^a_bf(x)dx = f(ξ)(b-a)