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around the boundary of o of the vector field F = (9x − 6y)i + (6y – 2z)j + (2z - 9x) k in two ways: first, calculate the line integral directly; second, use Stokes' Theorem. 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, going from the x axis to the y axis) is parameterized by 0 C₂ (the edge following C₁, going from the y axis to the z axis) is parameterized by 0 C3 (the last edge, from the z axis to the x axis) is parameterized by 0 F. dr = 0 lá F. dr = 0 F. dr = 0 C3 1.² 0 F. dr = 0 STOKES' THEOREM o may be parameterized by r(u, v) = (u, v, 7-3u-70), where the domain of the parametrization is the triangle in the uv-plane with vertices (0,0), (7,0), (0,7). 5 curl F = 0 0 (curl F). ds = = 0 J 0 0 0 0 du du

around the boundary of o of the vector field F = (9x − 6y)i + (6y – 2z)j + (2z - 9x) k in two ways: first, calculate the line integral directly; second, use Stokes' Theorem. 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, going from the x axis to the y axis) is parameterized by 0 C₂ (the edge following C₁, going from the y axis to the z axis) is parameterized by 0 C3 (the last edge, from the z axis to the x axis) is parameterized by 0 F. dr = 0 lá F. dr = 0 F. dr = 0 C3 1.² 0 F. dr = 0 STOKES' THEOREM o may be parameterized by r(u, v) = (u, v, 7-3u-70), where the domain of the parametrization is the triangle in the uv-plane with vertices (0,0), (7,0), (0,7). 5 curl F = 0 0 (curl F). ds = = 0 J 0 0 0 0 du du

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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around the boundary of o of the vector field F = (9x − 6y)i + (6y – 2z) j + (2z − 9x) k in two ways: first, calculate the line integral directly; second, use Stokes' Theorem. 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, going from the x axis to the y axis) is parameterized by 0 C₂ (the edge following C₁, going from the y axis to the z axis) is parameterized by 0 C3 (the last edge, from the z axis to the x axis) is parameterized by 0 Ja Ja Ja lo F. dr = 0 F. dr = 0 F. dr = 0 F. dr = 0 STOKES' THEOREM b 7-3u-7v o may be parameterized by r(u, v) = (u, v, 3u-7°), where the domain of the parametrization is the triangle in the uv-plane with vertices (0, 0), (3,0), (0,7). curl F = 0 ər ər ди X = 0 du 0 J (curl F). ds = [ 0 = 0 0 0 0 du du
Transcribed Image Text:around the boundary of o of the vector field F = (9x − 6y)i + (6y – 2z) j + (2z − 9x) k in two ways: first, calculate the line integral directly; second, use Stokes' Theorem. 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, going from the x axis to the y axis) is parameterized by 0 C₂ (the edge following C₁, going from the y axis to the z axis) is parameterized by 0 C3 (the last edge, from the z axis to the x axis) is parameterized by 0 Ja Ja Ja lo F. dr = 0 F. dr = 0 F. dr = 0 F. dr = 0 STOKES' THEOREM b 7-3u-7v o may be parameterized by r(u, v) = (u, v, 3u-7°), where the domain of the parametrization is the triangle in the uv-plane with vertices (0, 0), (3,0), (0,7). curl F = 0 ər ər ди X = 0 du 0 J (curl F). ds = [ 0 = 0 0 0 0 du du
Let o be the surface 3x + 7y + 5z = 7 in the first octant, oriented upwards. Let C be the oriented boundary of o. Compute the line integral he boundary of o of the vector field F = (9x − 6y) i + (6y − 2z) j + (2z – 9x) k in two ways: first, calculate the line integral directly; second, Kes' Theorem.
Transcribed Image Text:Let o be the surface 3x + 7y + 5z = 7 in the first octant, oriented upwards. Let C be the oriented boundary of o. Compute the line integral he boundary of o of the vector field F = (9x − 6y) i + (6y − 2z) j + (2z – 9x) k in two ways: first, calculate the line integral directly; second, Kes' Theorem.
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