Work Along a Path

Line integrals

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Work along a path: W = ∫ F · dr = ∫ (P dx + Q dy).
• Only the part of F along the path counts.
• In some fields, like whirls, the work depends on the path.

Steps

1. Adding up pushes
2. A constant force
3. The path matters
4. Once around
5. Crossing the wind
6. An integral by hand