Referring to Figure 24 , suppose that (oint_{C_{2}} mathbf{F} cdot d mathbf{r}=12). Use Green's Theorem to determine

Question:

Referring to Figure 24 , suppose that $\oint_{C_{2}} \mathbf{F} \cdot d \mathbf{r}=12$. Use Green's Theorem to determine $\oint_{C_{1}} \mathbf{F} \cdot d \mathbf{r}$, assuming that $\frac{\partial F_{2}}{\partial x}-\frac{\partial F_{1}}{\partial y}=-3$ in $\mathcal{D}$.

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