Let (mathcal{S}) be the oriented half-cylinder in Figure 15. In (a)-(f), determine whether (iint_{mathcal{S}} mathbf{F} cdot d

Question:

Let $\mathcal{S}$ be the oriented half-cylinder in Figure 15. In (a)-(f), determine whether $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$ is positive, negative, or zero. Explain your reasoning.
(a) $\mathbf{F}=\mathbf{i}$
(b) $\mathbf{F}=\mathbf{j}$
(c) $\mathbf{F}=\mathbf{k}$
(d) $\mathbf{F}=y \mathbf{i}$
(e) $\mathbf{F}=-y \mathbf{j}$
(f) $\mathbf{F}=x \mathbf{j}$

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