(a) Find the flux of the vector field F across the enclosed surface S. Sketch the surface. F = yi + 3xj+4zk, and S is the boundary of the solid region enclosed by z=7-x² - y² and the plane z = 4. (note that this includes two surfaces). Assume outward orientation. Do not use the Divergence Theorem. Evaluate completely.

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Chapter2: Second-order Linear Odes
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Please show work. This is my calculus 3 hw. Part A
(a) Find the flux of the vector field F across the enclosed surface S. Sketch the surface.
F = yi + 3x j + 4zk, and S is the boundary of the solid region enclosed by z=7-x² - y² and the
plane z = 4. (note that this includes two surfaces). Assume outward orientation. Do not use the
Divergence Theorem. Evaluate completely.
(b) Use the Divergence Theorem to SET UP another integral that can be used to solve the problem in
part (a). You do not need to evaluate the integral. Include all bounds and variables of integration.
Transcribed Image Text:(a) Find the flux of the vector field F across the enclosed surface S. Sketch the surface. F = yi + 3x j + 4zk, and S is the boundary of the solid region enclosed by z=7-x² - y² and the plane z = 4. (note that this includes two surfaces). Assume outward orientation. Do not use the Divergence Theorem. Evaluate completely. (b) Use the Divergence Theorem to SET UP another integral that can be used to solve the problem in part (a). You do not need to evaluate the integral. Include all bounds and variables of integration.
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