Find the line integrals of F = 3yi + xj + 3zk from (0,0,0) to (1,1,1) over each of the following paths. a. The straight-line path C₁: r(t) = ti + tj + tk, 0st≤1 b. The curved path C₂: r(t) = ti + t²j+tªk, 0sts1 c. The path C3UC4 consisting of the line segment from (0,0,0) to (1,1,0) followed by the segment from (1,1,0) to (1,1,1) (0, 0, 0) C₁ (1, 1, 1) C₁
Find the line integrals of F = 3yi + xj + 3zk from (0,0,0) to (1,1,1) over each of the following paths. a. The straight-line path C₁: r(t) = ti + tj + tk, 0st≤1 b. The curved path C₂: r(t) = ti + t²j+tªk, 0sts1 c. The path C3UC4 consisting of the line segment from (0,0,0) to (1,1,0) followed by the segment from (1,1,0) to (1,1,1) (0, 0, 0) C₁ (1, 1, 1) C₁
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:Find the line integrals of F = 3yi + xj + 3zk
from (0,0,0) to (1,1,1) over each of the
following paths.
a. The straight-line path C₁: r(t) = ti + tj + tk,
0sts1
b. The curved path C₂: r(t) = ti + t²j+tªk,
0sts1
c. The path C3UC4 consisting of the line
segment from (0,0,0) to (1,1,0) followed by
the segment from (1,1,0) to (1,1,1)
(0, 0, 0)
C₁
(1, 1, 1)
|C₂
(1, 1, 0)
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