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Question

# Use Green's Theorem to prove the plane case of Theorem 14.3D; that is, show that $\partial N / \partial x=\partial M / \partial y$ implies that $\oint_C M d x+N d y=0$, which implies that $\mathbf{F}=M \mathbf{i}+N \mathbf{j}$ is conservative.

Solution

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In this problem, we have to show that $\textbf{F}=\left$ is conservative, if the following is true:

$\dfrac{\partial N}{\partial x}=\dfrac{\partial M}{\partial y}$

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