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2x c. S 0 9dt 2x D.D. S- 18 dt Construct the surface integral of Stokes' Theorem using R = {(x,y): x² + y² ≤9} as the region of integration. Choose the correct answer below. MA -2ffan dA R DR-effen B. dA Scaffon R CC dA

2x c. S 0 9dt 2x D.D. S- 18 dt Construct the surface integral of Stokes' Theorem using R = {(x,y): x² + y² ≤9} as the region of integration. Choose the correct answer below. MA -2ffan dA R DR-effen B. dA Scaffon R CC dA

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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Verify that the line integral and the surface integral of Stokes' Theorem are equal for the following vector field, surface S, and closed curve C. Assume that C has counterclockwise orientation and S has a consistent orientation. F = (y, - x, 7); S is the upper half of the sphere x² + y² + z² = 9 and C is the circle x² + y² = 9 in the xy-plane. Construct the line integral of Stokes' Theorem using the parameterization r(t)= (3 cos t, 3 sin t,0), for 0 st≤2 for the curve C. Choose the correct answer below. 2π Jua 18 dt O A. B. O C. A. OB. 2π O C. 0 O D. O D. - 18 dt 2 Jam 9 dt o Construct the surface integral of Stokes' Theorem using R = {(x,y): x² + y² ≤9) as the region of integration. Choose the correct answer below. -zffan R - 9 dt 2π - 4√√ JA dA R JS JA R √ √ A R Evaluate both integrals to verify that they are equal. What is the result? (Type an exact answer, using as needed.)
Transcribed Image Text:Verify that the line integral and the surface integral of Stokes' Theorem are equal for the following vector field, surface S, and closed curve C. Assume that C has counterclockwise orientation and S has a consistent orientation. F = (y, - x, 7); S is the upper half of the sphere x² + y² + z² = 9 and C is the circle x² + y² = 9 in the xy-plane. Construct the line integral of Stokes' Theorem using the parameterization r(t)= (3 cos t, 3 sin t,0), for 0 st≤2 for the curve C. Choose the correct answer below. 2π Jua 18 dt O A. B. O C. A. OB. 2π O C. 0 O D. O D. - 18 dt 2 Jam 9 dt o Construct the surface integral of Stokes' Theorem using R = {(x,y): x² + y² ≤9) as the region of integration. Choose the correct answer below. -zffan R - 9 dt 2π - 4√√ JA dA R JS JA R √ √ A R Evaluate both integrals to verify that they are equal. What is the result? (Type an exact answer, using as needed.)
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