Vector Calculus

Green's Theorem in a plane relates a line integral around a simple closed curve $C$ to a double integral over the enclosed region $R$ as:

Options:

• (A) $\oint_C (M dx + N dy) = \iint_R \left( \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y} \right) dx dy$
• (B) $\oint_C (M dx + N dy) = \iint_R \left( \frac{\partial M}{\partial x} + \frac{\partial N}{\partial y} \right) dx dy$
• (C) $\oint_C (M dx + N dy) = 0$
• (D) $\oint_C (M dx + N dy) = \iint_R (M N) dx dy$