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

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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) \(\mathbf{F}=x \mathbf{j}\)

n X N

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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