AP Calculus BC / Unit 8: Applications of Integration
8.1 Finding the Average Value of a Function on an Interval
Notes
$$f_{avg}=\frac{1}{b-a}\int_a^b f(x)\,dx$$
- It's the height of the rectangle with the same area as the region under $f$.
Practice
Average value of $f(x)=x^2$ on $[0,3]$:
$\displaystyle \frac{1}{3}\cdot9=3$.
Average value of $\sin x$ on $[0,\pi]$:
$\displaystyle \frac{1}{\pi}\cdot2$.
The average value of velocity over $[a,b]$ equals:
$\displaystyle \frac{1}{b-a}\int v\,dt$.
Ready for more? Take the Unit 8 test.