Question: 7. Use Stokes's Theorem To Write Sc(2y2 + 6x4) Dx + (2x2 + 7...7. Use Stokes's Theorem to write ſ,(2y² + 6x*)dx + (2x² + 7y5)dy + (2zº – yz)dz as a surface integralwhere C is the boundary of the portion of the paraboloid z = 72 – 6x² – 6y² that is above the triangle withvertices at (0, 0), (3, 0) and (0, 3) oriented counterclockwise as viewed from above. Then set up a doubleintegral in terms of x and y that could be used to evaluate the surface integral. (Do not integrate.).Stokes's Theorem: Let S be an oriented surface with unit normal vector N, bounded by a piecewise smoothsimple closed curve C with a positive orientation. If F is a vector field whose component functions havecontinuous partial derivatives on an open region containing S and C, then [F dĩ = [[(§×F)- Ñ dS .

Answered: Image /qna-images/answer/34ff3986-3970-41ab-8f3b-0d2e3e9ebf06.jpg

7. Use Stokes's Theorem to write S.(2y² + 6x*)dx + (2x² + 7y³)dy+ (2z° – yz)dz as a surface integral where C is the boundary of the portion of the paraboloid z = 72 – 6x2 – 6y² that is above the triangle with vertices at (0, 0), (3, 0) and (0, 3) oriented counterclockwise as viewed from above. Then set up a double integral in tems of x and y that could be used to evaluate the surface integral. (Do not integrate.). Stokes's Theorem: Let S be an oriented surface with unit normal vector Ñ, bounded by a piecewise smooth simple closed curve C with a positive orientation. If F is a vector field whose component functions have continuous partial derivatives on an open region containing S and C, then [F dĩ = (ExF)-Ñ ds .

7. Use Stokes's Theorem to write S.(2y² + 6x*)dx + (2x² + 7y³)dy+ (2z° – yz)dz as a surface integral where C is the boundary of the portion of the paraboloid z = 72 – 6x2 – 6y² that is above the triangle with vertices at (0, 0), (3, 0) and (0, 3) oriented counterclockwise as viewed from above. Then set up a double integral in tems of x and y that could be used to evaluate the surface integral. (Do not integrate.). Stokes's Theorem: Let S be an oriented surface with unit normal vector Ñ, bounded by a piecewise smooth simple closed curve C with a positive orientation. If F is a vector field whose component functions have continuous partial derivatives on an open region containing S and C, then [F dĩ = (ExF)-Ñ ds .

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

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