Let f be a function that is integrable on the closed interval [a, b]. The mean value of f over the interval [a, b] is equal to

The mean value $\overline{y}$ has the property that the area under the curve y = f(x) between x = a and x = b is equal to the area under the horizontal line $y=\overline{y}$ between x = a and x = b, which is the area of a rectangle with width b − a and height $\overline{y}$.