Average Value of a Function (Leaving Cert Mathematics): Flashcards

It provides a single representative value over an interval.

Using $f_{avg} = \frac{1}{b-a} \int_a^b f(x) dx$.

It represents the total area under the curve $f(x)$.

It is the length of the interval used for scaling.

It represents the constant height enclosing area under $f(x)$.

Average value = $\frac{1}{b-a} \int_{a}^{b} f(x) dx$

Average value = $\frac{1}{b-a} \int_a^b f(x) dx$

Identify the interval $[a, b]$ and the function $f(x)$.

Used in physics, engineering, and economics for averages.

Divide the result by the interval length $b - a$.