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straight-line path

straight-line path

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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Find the line integral of F = 4√√zi - 2xj + √yk, 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, 0≤t≤1 b. The curved path C₂: r(t) = ti + t²j + tªk, 0≤t≤1 c. The path C3 UC4 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) (1, 1, 0)
Transcribed Image Text:Find the line integral of F = 4√√zi - 2xj + √yk, 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, 0≤t≤1 b. The curved path C₂: r(t) = ti + t²j + tªk, 0≤t≤1 c. The path C3 UC4 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) (1, 1, 0)
Find the line integrals of F = 2yi + 3xj + zk 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, 0≤t≤ 1 b. The curved path C₂: r(t) = ti + t²j+t¹k, 0≤t≤1 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) } (1, 1, 1) CA (1, 1, 0)
Transcribed Image Text:Find the line integrals of F = 2yi + 3xj + zk 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, 0≤t≤ 1 b. The curved path C₂: r(t) = ti + t²j+t¹k, 0≤t≤1 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) } (1, 1, 1) CA (1, 1, 0)
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