10.Consider the closed, solid region E between the paraboloid z = 4 – x? – y? and the xy-plane,and consider the vector field F(x,y, z) = (2z, y, y²). Determine the exact value of Sf,F. dS, where S is theboundary of E. (Hint: Take advantage of the fact that the surface is closed.)

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Consider the closed, solid region E between the paraboloid z = 4 – x? – y? and the xy-plane, and consider the vector field F(x,y, z) = (2z, y, y?). Determine the exact value of [f,F · dS, where S is the boundary of E. (Hint: Take advantage of the fact that the surface is closed.)

Consider the closed, solid region E between the paraboloid z = 4 – x? – y? and the xy-plane, and consider the vector field F(x,y, z) = (2z, y, y?). Determine the exact value of [f,F · dS, where S is the boundary of E. (Hint: Take advantage of the fact that the surface is closed.)

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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Question

10.
Consider the closed, solid region E between the paraboloid z = 4 – x? – y? and the xy-plane,
and consider the vector field F(x,y, z) = (2z, y, y²). Determine the exact value of Sf,F. dS, where S is the
boundary of E. (Hint: Take advantage of the fact that the surface is closed.)

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