Verify Stokes' theorem for the helicoid Y(r, 0) = (r cos 0, r sin 0, 0) where (r, 0) lies in the rectangle [0, 1] × [0, л/2], and F is the vector field F = (7z, 8x, 4y). First, compute the surface integral: (V × F) · dS = få ſå ƒ(r, 0)dr d0, where a = b = f(r, 0) = Finally, the value of the surface integral is , C = g(0) = Next compute the line integral on that part of the boundary from (1, 0, 0) to (0, 1, л/2). ScF. dr = = g(0) do, where a = ,b= d = (use "t" for theta). and (use "t" for theta). , and
Verify Stokes' theorem for the helicoid Y(r, 0) = (r cos 0, r sin 0, 0) where (r, 0) lies in the rectangle [0, 1] × [0, л/2], and F is the vector field F = (7z, 8x, 4y). First, compute the surface integral: (V × F) · dS = få ſå ƒ(r, 0)dr d0, where a = b = f(r, 0) = Finally, the value of the surface integral is , C = g(0) = Next compute the line integral on that part of the boundary from (1, 0, 0) to (0, 1, л/2). ScF. dr = = g(0) do, where a = ,b= d = (use "t" for theta). and (use "t" for theta). , and
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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![Verify Stokes' theorem for the helicoid Y(r, 0) = (r cos 0, r sin 0, 0) where (r, 0) lies in the rectangle [0, 1] × [0, π/2], and F is the vector field
F = (7z, 8x, 4y).
First, compute the surface integral:
JMVXF). ds = f f f(r, 0)dr do, where
a =
b =
=
f(r, 0) =
Finally, the value of the surface integral is
g(0) =
, C =
Next compute the line integral on that part of the boundary from (1, 0, 0) to (0, 1, à/2).
ſcF · dr = ſå g(0) d0, where
a =
,b=
d =
(use "t" for theta).
and
(use "t" for theta).
and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5986935-b6be-4a96-bfb6-ef1e2a130287%2F02351076-9e9c-42f5-985e-a2236813d3f6%2Fbxzszgh_processed.png&w=3840&q=75)
Transcribed Image Text:Verify Stokes' theorem for the helicoid Y(r, 0) = (r cos 0, r sin 0, 0) where (r, 0) lies in the rectangle [0, 1] × [0, π/2], and F is the vector field
F = (7z, 8x, 4y).
First, compute the surface integral:
JMVXF). ds = f f f(r, 0)dr do, where
a =
b =
=
f(r, 0) =
Finally, the value of the surface integral is
g(0) =
, C =
Next compute the line integral on that part of the boundary from (1, 0, 0) to (0, 1, à/2).
ſcF · dr = ſå g(0) d0, where
a =
,b=
d =
(use "t" for theta).
and
(use "t" for theta).
and
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