1. Set up the integral: $\int_{a}^{b} f(x) , dx$. 2. Multiply by $\frac{1}{b-a}$. 3. Evaluate the expression.

Identify the interval [a,b] and the function f(x). Then setup: $\frac{1}{b-a} \int_{a}^{b} f(x) , dx$

It finds the height of a rectangle with the same width (b-a) as the interval [a, b] that has the same area as the area under the curve of the function on that interval.

The area under the curve of f(x) from x=a to x=b.

Continuity ensures that the definite integral exists and that the average value can be accurately calculated.

The average y-value of a function over a given interval.

The function has no breaks, jumps, or undefined points on the closed interval from a to b.

The definite integral of a function f(x) from a to b represents the net signed area between the curve of f(x) and the x-axis from x=a to x=b.