Suppose S is the surface in R³ that is the part of the ellipsoid 4x² + y² + 9z² = 37 satisfying y ≥ 1, and let F(x, y, z) be the vector field defined by F(x, y, z) = (y, ln(y) + 2² sin(ry), -x). We want to compute JI, 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. i. ii. iii. curlFnds. 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 is consistent with the orientation of S.
Suppose S is the surface in R³ that is the part of the ellipsoid 4x² + y² + 9z² = 37 satisfying y ≥ 1, and let F(x, y, z) be the vector field defined by F(x, y, z) = (y, ln(y) + 2² sin(ry), -x). We want to compute JI, 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. i. ii. iii. curlFnds. 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 is consistent with the orientation of S.
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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