For each of the line integrals covered in class, give a formula, assuming that the curve C has a parameterization r(t), where t€ [a,b]. The scalar line integral of f along C, [f(x, y, z)ds The vector line integral of a vector field F = Mi+Nj+Pk along C, [ F. dr = [ F • Tds = [ M M dx + N dy + P dz The (two-dimensional) flux integral of a vector field F = Mi+Nj across C, [F = [₁ M C C F.nds = M dy – N dx
For each of the line integrals covered in class, give a formula, assuming that the curve C has a parameterization r(t), where t€ [a,b]. The scalar line integral of f along C, [f(x, y, z)ds The vector line integral of a vector field F = Mi+Nj+Pk along C, [ F. dr = [ F • Tds = [ M M dx + N dy + P dz The (two-dimensional) flux integral of a vector field F = Mi+Nj across C, [F = [₁ M C C F.nds = M dy – N dx
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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Question
#1
![For each of the line integrals covered in class, give a formula, assuming that the curve C has a
parameterization
r(t), where t = [a, b].
The scalar line integral of f along C,
The vector line integral of a vector field F = Mi+Nj+Pk along C,
-6₁
C
La
[f(x, y, z) ds
F.dr =
F.Tds =
Ja M dx + N dy +Pdz
The (two-dimensional) flux integral of a vector field F = Mi+Nj across C,
[F.nds = [ Mdy - N](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa68164dd-6bba-4aa5-92bc-4824a71db092%2F0768de7e-62a8-40f4-801a-6aa235499f56%2Fjwldwy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For each of the line integrals covered in class, give a formula, assuming that the curve C has a
parameterization
r(t), where t = [a, b].
The scalar line integral of f along C,
The vector line integral of a vector field F = Mi+Nj+Pk along C,
-6₁
C
La
[f(x, y, z) ds
F.dr =
F.Tds =
Ja M dx + N dy +Pdz
The (two-dimensional) flux integral of a vector field F = Mi+Nj across C,
[F.nds = [ Mdy - N
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