Let (mathcal{S}) be the disk (x^{2}+y^{2} leq 1) in the (x y)-plane oriented with normal in the
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Let \(\mathcal{S}\) be the disk \(x^{2}+y^{2} \leq 1\) in the \(x y\)-plane oriented with normal in the positive \(z\)-direction. Determine \(\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}\) for each of the following vector constant fields:
(a) \(\mathbf{F}=\langle 1,0,0angle\)
(b) \(\mathbf{F}=\langle 0,0,1angle\)
(c) \(\mathbf{F}=\langle 1,1,1angle\)
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