Practice question · Match the pairs
Match each integral theorem to its dimensionality.
- Fundamental theorem of calculus
- Green's theorem
- Stokes' theorem
- Divergence theorem
- 3D: surface integral ↔ volume integral
- 1D: − =
- 2D: line integral ↔ area integral
- 3D: line integral ↔ surface integral
Hints
- Order them by the dimension of the region being integrated over.
- Each theorem relates a boundary to the interior it bounds.
Show the answer
- Fundamental theorem of calculus → 1D: − =
- Green's theorem → 2D: line integral ↔ area integral
- Stokes' theorem → 3D: line integral ↔ surface integral
- Divergence theorem → 3D: surface integral ↔ volume integral
Why
Each theorem relates a boundary integral to an interior integral, at increasing dimension.
Practise Stokes' Theorem
The app has 9 more questions on this lesson, and keeps your place in the course. Physics I is free to start.