average value
[average value|average value] [average value] is defined as the integral of a function over an interval [a, b], divided by the length of the interval, for a continuous function f(x).
Definition
average value [average value] is defined as the integral of a function over an interval [a, b], divided by the length of the interval, for a continuous function f(x).
Mechanism
average value The average value of a linear function over an interval is calculated by integrating the function across the interval and dividing by the interval length. Example 5.14 demonstrates this process using f(x) = x + 1 over [0, 5].
Effects
average value [average value] affects the calculation of a function's integral over an interval, as demonstrated by the formula involving feoax and b-an. The definition requires continuity of f(x) on [a, b] for the average value to be valid.