Let o be the surface 4x + 6y + 8z = 5 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 o through the vector field F = (7x - 6y)i + (6y − 8z)j + (8z – 7x)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 o 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 Sai F. dr = Ja F.dr = Je₂ F.dr = fo F.dr = STOKES' THEOREM o may be parameterized by r(x, y) = (x, y, f(x, y)) = | curl F = ox ff (c (curl F) · ndS= TIO dydz
Let o be the surface 4x + 6y + 8z = 5 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 o through the vector field F = (7x - 6y)i + (6y − 8z)j + (8z – 7x)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 o 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 Sai F. dr = Ja F.dr = Je₂ F.dr = fo F.dr = STOKES' THEOREM o may be parameterized by r(x, y) = (x, y, f(x, y)) = | curl F = ox ff (c (curl F) · ndS= TIO dydz
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:Let o be the surface 4x + 6y + 8z = 5 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 o
through the vector field F = (7x − 6y)i + (6y − 8z)j + (8z - 7a)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
Jai
F.dr =
Joi
√dr=0
F. dr :
le
F.dr =
F.dr =
STOKES' THEOREM
o may be parameterized by r(x, y) = (x, y, f(x, y)) =
curl F =
arx
ff (curl F) · nds:
d
II
dy dx
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