Let (partial mathcal{R}) be the boundary of the rectangle in Figure 1, and let (partial mathcal{R}_{1}) and

Question:

Let $\partial \mathcal{R}$ be the boundary of the rectangle in Figure 1, and let $\partial \mathcal{R}_{1}$ and $\partial \mathcal{R}_{2}$ be the boundaries of the two triangles, all oriented counterclockwise.

(a) Determine $\oint_{\partial \mathcal{R}_{1}} \mathbf{F} \cdot d \mathbf{r}$ if $\oint_{\partial \mathcal{R}} \mathbf{F} \cdot d \mathbf{r}=4$ and $\oint_{\partial \mathcal{R}_{2}} \mathbf{F} \cdot d \mathbf{r}=-2$.
(b) What is the value of $\oint_{\partial \mathcal{R}} \mathbf{F} d \mathbf{r}$ if $\partial \mathcal{R}$ is oriented clockwise?

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