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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 =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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D is some triangular domain in the xy-plane with area equal to 9. S is 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 =
Transcribed Image Text:D is some triangular domain in the xy-plane with area equal to 9. S is 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 =
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