Verify Stokes' theorem for the helicoid (1, 0) = First, compute the surface integral: = (VF) Sff(r.)dr de, where a = 0 f(r,0)= b = pi/2 Finally, the value of the surface integral is (r cos 0, r sin 0, 0) where (r, 6) lies in the rectangle [0, 1] × [0, π/2], and F is the vector field F = (8z, 7x, 2y). ,c=0 ,d=1 , and (use "t" for theta). Next compute the line integral on that part of the boundary from (1,0,0) to (0, 1, π/2). SF dr=f9(6) do, where a=0 9(0) = b = , and (use "t" for theta).
Verify Stokes' theorem for the helicoid (1, 0) = First, compute the surface integral: = (VF) Sff(r.)dr de, where a = 0 f(r,0)= b = pi/2 Finally, the value of the surface integral is (r cos 0, r sin 0, 0) where (r, 6) lies in the rectangle [0, 1] × [0, π/2], and F is the vector field F = (8z, 7x, 2y). ,c=0 ,d=1 , and (use "t" for theta). Next compute the line integral on that part of the boundary from (1,0,0) to (0, 1, π/2). SF dr=f9(6) do, where a=0 9(0) = b = , and (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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![Verify Stokes' theorem for the helicoid (1, 0) =
First, compute the surface integral:
=
(VF) Sff(r.)dr de, where
a=0
f(r,0)=
b = pi/2
Finally, the value of the surface integral is
(r cos 0, r sin 0, 0) where (r, 6) lies in the rectangle [0, 1] × [0, π/2], and F is the vector field F
=
(8z, 7x, 2y).
,c=0
,d=1
, and
(use "t" for theta).
Next compute the line integral on that part of the boundary from (1,0,0) to (0, 1, π/2).
SF dr=f9(6) do, where
a=0
9(0) =
b =
, and
(use "t" for theta).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd34a3692-a940-49c3-89f7-41b744f50407%2F6bda9372-e66a-4e57-8acb-90b13978ef24%2Ffhugml_processed.png&w=3840&q=75)
Transcribed Image Text:Verify Stokes' theorem for the helicoid (1, 0) =
First, compute the surface integral:
=
(VF) Sff(r.)dr de, where
a=0
f(r,0)=
b = pi/2
Finally, the value of the surface integral is
(r cos 0, r sin 0, 0) where (r, 6) lies in the rectangle [0, 1] × [0, π/2], and F is the vector field F
=
(8z, 7x, 2y).
,c=0
,d=1
, and
(use "t" for theta).
Next compute the line integral on that part of the boundary from (1,0,0) to (0, 1, π/2).
SF dr=f9(6) do, where
a=0
9(0) =
b =
, and
(use "t" for theta).
![Find
F. dr where C is a circle of radius 3 in the plane x + y + z = 4, centered at (3, 3, -2) and oriented clockwise when viewed from the origin, if
F= 4yi 3x]+(y − x)k
-
Sc F.dr =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd34a3692-a940-49c3-89f7-41b744f50407%2F6bda9372-e66a-4e57-8acb-90b13978ef24%2Ftwzh4ta_processed.png&w=3840&q=75)
Transcribed Image Text:Find
F. dr where C is a circle of radius 3 in the plane x + y + z = 4, centered at (3, 3, -2) and oriented clockwise when viewed from the origin, if
F= 4yi 3x]+(y − x)k
-
Sc F.dr =
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