Find the flow rate of F =< y°z, -xy, x+y+z > across the portion of the surface z = over the unit square [0, 1] × [0, 1] in the ry-plane. Let the surface be oriented by the normal pointing upwards. ye" lying
Find the flow rate of F =< y°z, -xy, x+y+z > across the portion of the surface z = over the unit square [0, 1] × [0, 1] in the ry-plane. Let the surface be oriented by the normal pointing upwards. ye" lying
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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3
![(a) Find the flow rate of F =< y°z, –xy, x+y+z > across the portion of the surface z =
over the unit square [0, 1] × [0, 1] in the xy-plane. Let the surface be oriented by the normal
pointing upwards.
ye" lying
(b) Use Stokes' theorem to £nd the work done by the vector field F =< xyz-e",-xyz, x²yz+sin z >
on a particle that moves on the ii segments from (0,0, 1) to (1,1, 1) to (0,0, 2) and back to
(0,0,0).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0334823-d1ad-406c-8580-9ec7bca1a6cd%2F7bfe567d-5fbe-411e-93df-5afd710e03f2%2Fui845zk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Find the flow rate of F =< y°z, –xy, x+y+z > across the portion of the surface z =
over the unit square [0, 1] × [0, 1] in the xy-plane. Let the surface be oriented by the normal
pointing upwards.
ye" lying
(b) Use Stokes' theorem to £nd the work done by the vector field F =< xyz-e",-xyz, x²yz+sin z >
on a particle that moves on the ii segments from (0,0, 1) to (1,1, 1) to (0,0, 2) and back to
(0,0,0).
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