?Use the divergence theorem to evaluate \(\iint_{S} \mathbf{F} \cdot d
Chapter 6, Problem 447(choose chapter or problem)
Use the divergence theorem to evaluate \(\iint_{S} \mathbf{F} \cdot d S\).
\(\mathbf{F}(x, y, z)=(2 x y) \mathbf{i}+\left(-y^{2}\right) \mathbf{j}+\left(2 z^{3}\right) \mathbf{k}\), where S is bounded by paraboloid \(z=x^{2}+y^{2}\) and plane z = 2
Text Transcription:
iint_S F cdot dS
F (x, y, z)=(2xy)i + (-y^2)j + (2z^3)k
z=x^2 + y^2
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