Discussion
Match the theorem with the pair of integrals it connects. 1. Green 2. Stokes 3. Gauss divergence P. Closed line integral and flux of a curl Q. Closed plane line integral and area integral R. Closed surface flux and volume integral
Answer: C
Green's theorem is the plane case, trading a boundary line integral for an integral over the enclosed area. Stokes lifts it into space, the area integral becoming a flux of the curl through a spanning surface. Gauss relates a closed surface to the volume it encloses, and has no boundary curve at all
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