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Average Value of a Function

Definition

The average value of a function over an interval is the total change in the function divided by the length of the interval.

Analogy

Imagine you are driving a car and you want to know your average speed for a trip. You would calculate it by dividing the total distance traveled by the time it took. Similarly, finding the average value of a function is like finding its average "speed" over an interval.

Related terms

Particle Motion: Refers to the movement of an object along a path. It can be described using functions that represent position, velocity, and acceleration.

Net Change: Represents the overall difference or total amount of change in a quantity over an interval. It can be calculated by subtracting initial value from final value.

Definite Integral: In calculus, it represents the signed area between a curve and x-axis over an interval. It can also be used to find average values and net changes.