In
calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
, and especially
multivariable calculus
Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving several variables, rather ...
, the mean of a function is loosely defined as the average value of the
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-oriente ...
over its
domain. In one variable, the mean of a function ''f''(''x'') over the
interval (''a'',''b'') is defined by
:
Recall that a defining property of the average value
of finitely many numbers
is that
. In other words,
is the ''constant'' value which when
''added'' to itself
times equals the result of adding the
terms
. By analogy, a
defining property of the average value
of a function over the interval