Verify Stokes' theorem for the helicoid ¥(r,0) = (r cos 0, r sin 0,0) where (r, 0) lies in the rectangle [0, 1] × [0, 7/2], and F is the vector field F = (7z, 9x, 2y). First, compute the surface integral: Slu(V × F) · dS = Si S“ f(r,0)dr dO, where 出,b= d = , and a .c= f(r, 0) = (use "t" for theta). Finally, the value of the surface integral is Next compute the line integral on that part of the boundary from (1, 0, 0) to (0, 1, 7/2). S¢F•dr = [, g(0) d0 , where a = ,b= , and g(0) (use "t" for theta).
Verify Stokes' theorem for the helicoid ¥(r,0) = (r cos 0, r sin 0,0) where (r, 0) lies in the rectangle [0, 1] × [0, 7/2], and F is the vector field F = (7z, 9x, 2y). First, compute the surface integral: Slu(V × F) · dS = Si S“ f(r,0)dr dO, where 出,b= d = , and a .c= f(r, 0) = (use "t" for theta). Finally, the value of the surface integral is Next compute the line integral on that part of the boundary from (1, 0, 0) to (0, 1, 7/2). S¢F•dr = [, g(0) d0 , where a = ,b= , and g(0) (use "t" for theta).
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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Question
![(r cos 0, r sin 0,0) where (r, 0) lies in the rectangle [0, 1] × [0, T/2], and F is the vector field
Verify Stokes' theorem for the helicoid V (r, 0)
F 3 (72, 9х, 2у).
First, compute the surface integral:
SIM (V × F) · dS = S. Sª f(r, 0)dr do, where
a =
,b =
.C=
d =
and
f(r, 0) =
(use "t" for theta).
Finally, the value of the surface integral is
Next compute the line integral on that part of the boundary from (1,0, 0) to (0, 1,T/2).
Sa F. dr = L" g(0) d0, where
a =
, and
g(0)
(use "t" for theta).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F19e11e41-17de-428a-b835-39e3ad648d81%2F07506e47-ba30-4fb3-8ece-05aec7c057d9%2Ff1t2b7k_processed.png&w=3840&q=75)
Transcribed Image Text:(r cos 0, r sin 0,0) where (r, 0) lies in the rectangle [0, 1] × [0, T/2], and F is the vector field
Verify Stokes' theorem for the helicoid V (r, 0)
F 3 (72, 9х, 2у).
First, compute the surface integral:
SIM (V × F) · dS = S. Sª f(r, 0)dr do, where
a =
,b =
.C=
d =
and
f(r, 0) =
(use "t" for theta).
Finally, the value of the surface integral is
Next compute the line integral on that part of the boundary from (1,0, 0) to (0, 1,T/2).
Sa F. dr = L" g(0) d0, where
a =
, and
g(0)
(use "t" for theta).
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