Average-Value

Definition

The average-value of a function over an interval is the value that represents the average height of the function over that interval. It can be found by dividing the total area under the curve of the function on that interval by the length of the interval.

Related terms

Definite Integral:

A definite integral is used to find accumulated change or total area under a curve between two specific points.

Riemann Sum:

A Riemann sum is an approximation method for finding definite integrals using subintervals and sample points within those subintervals.

Mean Value Theorem:

The Mean Value Theorem states that if a function is continuous on a closed interval and differentiable on an open interval, then there exists at least one point in that interval where instantaneous rate of change (derivative) equals its average rate of change (slope between endpoints).