Calculus
Advanced

Average Value of a Function

The mean value of a continuous function over an interval.

Formula

favg=1b−a∫abf(x) dxf_{avg} = \frac{1}{b-a}\int_a^b f(x)\,dx

Variables

fFunction
a, bLimits

Example

The average of f(x) = x on [0, 4] is (1/4)∫₀⁴ x dx = (1/4)·8 = 2.

Did You Know?

Calculus can find the average height of a curve — the level at which its area would be a rectangle.

integralaverage