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).
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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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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fe1fc35-672a-49fd-831b-9642c77888ed%2Ff57ef952-0dfa-4a97-85b3-4ebcd928c002%2Faiht44q_processed.png&w=3840&q=75)
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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