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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
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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(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).
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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