Let o be the surface 4x + 5y +9z= 7 in the first octant, oriented upwards. Let C be the oriented boundary of a. Compute the work done in moving a unit mass particle around the boundary of a through the vector field F = (2x-3y)i + (3y-8z)j + (8z-2x) k using line integrals, and using Stokes' Theorem. Assume mass is measured in kg, length in meters, and force in Newtons (1 nt = 1kg-m). LINE INTEGRALS Parameterize the boundary of a positively using the standard form, tv+P with 0≤t≤ 1, starting with the segment in the xy plane. C₁ (the edge in the xy plane) is parameterized by C₂ (the edge following C₁) is parameterized by C (the last edge) is parameterized by Joi √ F Jo₂² F-dr= F.dr= F.dr= F.dr=
Let o be the surface 4x + 5y +9z= 7 in the first octant, oriented upwards. Let C be the oriented boundary of a. Compute the work done in moving a unit mass particle around the boundary of a through the vector field F = (2x-3y)i + (3y-8z)j + (8z-2x) k using line integrals, and using Stokes' Theorem. Assume mass is measured in kg, length in meters, and force in Newtons (1 nt = 1kg-m). LINE INTEGRALS Parameterize the boundary of a positively using the standard form, tv+P with 0≤t≤ 1, starting with the segment in the xy plane. C₁ (the edge in the xy plane) is parameterized by C₂ (the edge following C₁) is parameterized by C (the last edge) is parameterized by Joi √ F Jo₂² F-dr= F.dr= F.dr= F.dr=
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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Transcribed Image Text:STOKES' THEOREM
o may be parameterized by r(x, y) = (r, y, f(x, y)) =
curl F =
(curl F) . nds =
TIO dy dr
00
Transcribed Image Text:Let o be the surface 4x + 5y +9z=7 in the first octant, oriented upwards. Let C be the oriented boundary of o.
Compute the work done in moving a unit mass particle around the boundary of a through the vector field
F = (2x-3y)i + (3y-82)j + (8z-2x)k using line integrals, and using Stokes' Theorem.
Assume mass is measured in kg, length in meters, and force in Newtons (1 nt = 1kg-m).
LINE INTEGRALS
Parameterize the boundary of or positively using the standard form, tv+P with 0≤t≤ 1, starting with the segment in the
xy plane.
C₁ (the edge in the xy plane) is parameterized by
C2 (the edge following C₁) is parameterized by
C3 (the last edge) is parameterized by
Sa
F.dr=
SOF
-0
F dri
F.dr
F.dr=
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