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(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.

(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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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