Average Value

Definition

The average value of a continuous function f(x) over an interval [a, b] represents the height at which the graph would balance if it was folded along the x-axis. It can be calculated by dividing the definite integral of f(x) over [a, b] by the length of the interval (b - a).

Related terms

Definite Integral:

The definite integral is used to calculate accumulated quantities such as area under curves or total displacement over specific intervals.

Riemann Sum:

A Riemann sum approximates the area under a curve by dividing it into small rectangles and summing their areas.

Mean Value Theorem for Integrals: The Mean Value Theorem for Integrals states that if a function is continuous over an interval, then there exists at least one point within that interval where the instantaneous rate of change (derivative) equals the average rate of change (slope of secant line).