Question

mathematically the functions in Green's theorem will have​

Answer 1

Green's theorem gives a relationship between the line integral of a two-dimensional vector field over a closed path in the plane and the double integral over the region it encloses. The fact that the integral of a (two-dimensional) conservative field over a closed path is zero is a special case of Green's theorem .

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Answer 2

The functions in Green's theorem will have the continuous partial derivatives.

• Green's theorem gives a relationship between the line integral of a two-dimensional vector field over a closed path in the plane and the double integral over the region it encloses.
• The special case of Green's theorem is the fact that the integral of a (two-dimensional) conservative field over a closed path is zero.
• Green's theorem is the two-dimensional special case of Stokes' theorem.
• Stokes theorem is based on the principle of linking the macroscopic and microscopic circulations.
• Green’s theorem defines the relationship between the macroscopic circulation of curve C and the sum of the microscopic circulation.
• The microscopic circulation is inside the curve C.
• If L and M are functions of (x,y) in an open region containing D and having continuous partial derivatives.
• Then, ∫ (F dx + G dy) = ∫∫(dG/dx – dF/dy)dx dy can be taken anticlockwise.

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