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Green's theorem in the plane relates

  • A.a line integral round a closed curve to a double integral over the region it bounds
  • B.a surface integral to a volume integral over the region enclosed
  • C.a line integral to a surface integral over a spanning surface
  • D.two line integrals taken along different paths with the same endpoints

Answer: A

The theorem states

\[ \oint_{C}\left(M\,dx + N\,dy\right) \;=\; \iint_{R}\left(\frac{\partial N}{\partial x} - \frac{\partial M}{\partial y}\right)dA. \]

The other pairings describe Gauss's divergence theorem and Stokes's theorem, both of which are three-dimensional generalisations of this plane result

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