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STOKES' THEOREM o may be parameterized by r(r, y) = (1, y, f(x, y)) = curl F

STOKES' THEOREM o may be parameterized by r(r, y) = (1, y, f(x, y)) = curl F

Advanced Engineering Mathematics
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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STOKES' THEOREM o may be parameterized by r(2, y) = (z, y, f(x, y)) = curl F (curl F) - nds %3D dydz 54/(sqrt140)
Transcribed Image Text:STOKES' THEOREM o may be parameterized by r(2, y) = (z, y, f(x, y)) = curl F (curl F) - nds %3D dydz 54/(sqrt140)
Let o be the surface 10r + 2y + 6z = 8 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 o through the vector field F = (4x – 3y)i + (3y – 2)j + (z– 4x)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. C (the edge in the xy plane) is parameterized by <4/5-4/5t,41,0> C2 (the edge folowing C1) is parameterized by <0,4-41,4/3t> C3 (the last edge) is parameterized by <4/5t,0,4/3-4/3t> F dr= 688/25 C1 dr = -136/9 F-dr = dr= STOKES' THEOREM
Transcribed Image Text:Let o be the surface 10r + 2y + 6z = 8 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 o through the vector field F = (4x – 3y)i + (3y – 2)j + (z– 4x)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. C (the edge in the xy plane) is parameterized by <4/5-4/5t,41,0> C2 (the edge folowing C1) is parameterized by <0,4-41,4/3t> C3 (the last edge) is parameterized by <4/5t,0,4/3-4/3t> F dr= 688/25 C1 dr = -136/9 F-dr = dr= STOKES' THEOREM
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