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Different Forms of Line Integrals of Vector Fields The line integral SF - Tds may be expressed in the following forms, where F = (f, g, h) and C has a parameterization r(t) = (x(t), y(t), z(t)), for a ≤t≤ b: Line Integrals s(t) = . [ * F · r'(t) dt = [*(f(t)\z'(t) + g(t)y'(t) +h(t)z'(t)) dt = [ƒ dr- + gdy + h dz ds = s'(t) dt = For line integrals in the plane, we let F = (f, g) and assume C is parameterized in the form r(t) = (x(t), y(t)), for a ≤ t ≤ b. Then = [F which leads to: F. dr.

Different Forms of Line Integrals of Vector Fields The line integral SF - Tds may be expressed in the following forms, where F = (f, g, h) and C has a parameterization r(t) = (x(t), y(t), z(t)), for a ≤t≤ b: Line Integrals s(t) = . [ * F · r'(t) dt = [*(f(t)\z'(t) + g(t)y'(t) +h(t)z'(t)) dt = [ƒ dr- + gdy + h dz ds = s'(t) dt = For line integrals in the plane, we let F = (f, g) and assume C is parameterized in the form r(t) = (x(t), y(t)), for a ≤ t ≤ b. Then = [F which leads to: F. dr.

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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Different Forms of Line Integrals of Vector Fields The line integral SF.T ds may be expressed in the following forms, where F = (f, g, h) and C has a parameterization r(t) = (x(t), y(t), z(t)), for a ≤t≤ b: Line Integrals s(t) = [F. F.r' (t) dt = - [*(f(t)}x'(t) + g(t)y'(t) +h(t)z'(t)) dt a ds = s'(t) dt = = - [1 dz- с which leads to: f dx + gdy + h dz = - [F For line integrals in the plane, we let F = (f, g) and assume C is parameterized in the form r(t) = (x(t), y(t)), for a ≤ t ≤ b. Then F.dr.
Transcribed Image Text:Different Forms of Line Integrals of Vector Fields The line integral SF.T ds may be expressed in the following forms, where F = (f, g, h) and C has a parameterization r(t) = (x(t), y(t), z(t)), for a ≤t≤ b: Line Integrals s(t) = [F. F.r' (t) dt = - [*(f(t)}x'(t) + g(t)y'(t) +h(t)z'(t)) dt a ds = s'(t) dt = = - [1 dz- с which leads to: f dx + gdy + h dz = - [F For line integrals in the plane, we let F = (f, g) and assume C is parameterized in the form r(t) = (x(t), y(t)), for a ≤ t ≤ b. Then F.dr.
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