Calculus & Numerical Methods

Average Value of a Function

Mean value of f over [a, b].

Formula

Formula
f̄ = (1b−a) ∫ab f dx

Variables

SymbolDefinitionType & rangeUnitsRole
f function expression / text x input
a, b interval real number (ℝ) input

Try it yourself

Interactive calculator
math expression (e.g. x*x, sin(x))
Result

Worked examples

Example 1
Givenf(x) = x*x, a = 0, b = 3, intervals n = 1000
Result3.0000015
Example 2
Givenf(x) = sin(x), a = 0, b = 3.141592654, intervals n = 1000
Result0.6366192488