Mean Value Theorem for Integrals

Mean Value Theorem for Integrals

A variation of the mean value theorem which guarantees that a continuous function has at least one point where the function equals the average value of the function.

Mean Value Theorem for Integrals: if f is continuous on [a,b], there exists c in [a,b] such that f(c) = 1/(b−a) ∫f(x)dx

Graph showing y=f(x) curve over [a,b] with shaded area under curve equal to rectangle of height f(c), where c is between a and b.

See also

Theorem