D is some triangular domain in the xy-plane with area equal to 9. S i the triangular area that is cut out on the plane 5x + 3y + 1z = 100 in R3 by the vertical cylinder drawn over D. Let S be oriented with normal vectors pointing upwards. Let C be the boundary curve of S oriented positively for this orientation of S. Sketch a rough picture for your worksheet. (It does not have to be to scale) For the vector field F(x,y,z) = (x+4z)I + (x+y)j + (y+4z)k , work out F. dr First choose the method you propose to use: O Apply Stokes theorem, parametrize the surface and work out a surface integral O Somehow parametrize C and calculate the line integral O Apply the Fundamental Theorem for line integrals O Apply the Divergence Theorem and work out a triple integral O Apply Green's theorem and work out a double integral Then give the answer: F. dr =

D is some triangular domain in the xy-plane with area equal to 9. S i the triangular area that is cut out on the plane 5x + 3y + 1z = 100 in R3 by the vertical cylinder drawn over D. Let S be oriented with normal vectors pointing upwards. Let C be the boundary curve of S oriented positively for this orientation of S. Sketch a rough picture for your worksheet. (It does not have to be to scale) For the vector field F(x,y,z) = (x+4z)I + (x+y)j + (y+4z)k , work out F. dr First choose the method you propose to use: O Apply Stokes theorem, parametrize the surface and work out a surface integral O Somehow parametrize C and calculate the line integral O Apply the Fundamental Theorem for line integrals O Apply the Divergence Theorem and work out a triple integral O Apply Green's theorem and work out a double integral Then give the answer: F. dr =

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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