Integrals at Work

Averages, areas between curves, work

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Average value: $\frac{1}{b - a}\int_a^b f$.
• Area between curves: $\int (\text{top} - \text{bottom})\,dx$.
• Work done by a changing force: $\int F\,dx$. Distance: $\int v\,dt$.

Steps

1. Average of a function
2. Level it out
3. Area between two curves
4. Compute it
5. Work done by a changing force
6. Stretch a spring
7. Distance travelled