Suppose F x i y j (z 2 1) k and S is the surface of the region bounded by x2 y2 a2 , z

Chapter 9, Problem 62

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Suppose \(\mathbf{F}=x \mathbf{i}+y \mathbf{j}+\left(z^{2}+1\right) \mathbf{k}\) and S is the surface of the region bounded by \(x^{2}+y^{2}=a^{2}\), z = 0, z = c. Evaluate \(\iint_{S}(\mathbf{F} \cdot \mathbf{n}) d S\) without the aid of the divergence theorem. [Hint: The lateral surface area of the cylinder is \(2 \pi a c\).]

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