mean value theorem — An Etymological Dictionary of Astronomy and Astrophysics

mean value theorem

فربین ِ ارزش ِ میانگین

farbin-e arzeš-e miyângin

Fr.: théorème des accroissements finis

If f(x) is a continuous function on the interval from a to b, then:
∫ f(x) dx = f(c)(b - a) (summed from a to b) for at least one point in that interval.
More generally, If f(x) and g(x) are continuous functions on the interval from a to b and g(x)≥ 0, then:
∫ f(x)g(x) dx = f(c) ∫ g(x) dx (both integrals summed from a to b).

See also: → mean; → value; → theorem.

An Etymological Dictionary of Astronomy and Astrophysics