State and prove green's theorem

State and prove green’s theorem

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Statement of Green’s theorem

Green’s theorem is the extension of Stoke’s theorem and the divergence theorem. According to this theorem, if ϕ and ψ be the scalar functions, then

State and prove green's theorem

Proof of Green’s theorem

Let a vector

According to the divergence theorem.

Substituting the value of eqn. (2) in eqn. (1) we get

State and prove green's theorem

Which is the Green’s Theorem.