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Here, assume that S has the same orientation as defined by the positive orientatio of the ellipsoid. (a) Transform the surface integral to a line integral using Stokes Theorem. (b) i. ii. iii. curlF. curlF-nds. = [G. dr. (*) Find G(x, y, z) (*) Describe the relationship between S and C. (**) Provide a parametrisation r(t) of C so that its orientation consistent with the orientation of S. (**) Compute ff curlFnds using part (a).

Here, assume that S has the same orientation as defined by the positive orientatio of the ellipsoid. (a) Transform the surface integral to a line integral using Stokes Theorem. (b) i. ii. iii. curlF. curlF-nds. = [G. dr. (*) Find G(x, y, z) (*) Describe the relationship between S and C. (**) Provide a parametrisation r(t) of C so that its orientation consistent with the orientation of S. (**) Compute ff curlFnds using part (a).

Algebra & Trigonometry with Analytic Geometry
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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Need help with part b). Please explain each step and neatly type up. Thank you :)

 

4. Suppose S is the surface in R³ that is the part of the ellipsoid 4x² + y² + 9z² satisfying y ≥ 1, and let F(x, y, z) be the vector field defined by = 37 F(x, y, z) = (y, ln(y) + z² sin(ry), −x). We want to compute curlF.nds. Here, assume that S has the same orientation as defined by the positive orientation of the ellipsoid. (a) Transform the surface integral to a line integral using Stokes Theorem. (b) i. ii. iii. Ic curlFnds. = = [G. dr. (*) Find G(x, y, z) (*) Describe the relationship between S and C. (**) Provide a parametrisation r(t) of C so that its orientation is consistent with the orientation of S. (**) Compute ff curlF · ndS using part (a).
Transcribed Image Text:4. Suppose S is the surface in R³ that is the part of the ellipsoid 4x² + y² + 9z² satisfying y ≥ 1, and let F(x, y, z) be the vector field defined by = 37 F(x, y, z) = (y, ln(y) + z² sin(ry), −x). We want to compute curlF.nds. Here, assume that S has the same orientation as defined by the positive orientation of the ellipsoid. (a) Transform the surface integral to a line integral using Stokes Theorem. (b) i. ii. iii. Ic curlFnds. = = [G. dr. (*) Find G(x, y, z) (*) Describe the relationship between S and C. (**) Provide a parametrisation r(t) of C so that its orientation is consistent with the orientation of S. (**) Compute ff curlF · ndS using part (a).
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