Practice question · Multiple choice
Green’s theorem converts a line integral around a closed curve into a double integral over the region inside. Why is a CLOSED curve required?
Hints
- Ask what "the region inside" means for a curve with two loose ends.
- The theorem is about a boundary and what it bounds.
Show the answer
C. Because an open curve does not enclose a region
Why
Boundary and interior come as a pair. Stokes and the divergence theorem are the same idea in higher dimensions, and each needs a genuine boundary for the same reason.
Practise Green's Theorem
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More questions on Green's Theorem
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