Find the line integral of F = 2√√zi-4xj + 3√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≤ts1 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) 13 a. The line integral of F over the straight-line path C₁ is 9 (Type an integer or a simplified fraction.) (0, 0, 0) 9 (1, 1, 1) C₁ (1, 1, 0)
Find the line integral of F = 2√√zi-4xj + 3√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≤ts1 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) 13 a. The line integral of F over the straight-line path C₁ is 9 (Type an integer or a simplified fraction.) (0, 0, 0) 9 (1, 1, 1) C₁ (1, 1, 0)
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 integral of F = 2√√zi-4xj + 3√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≤ts1
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)
13
a. The line integral of F over the straight-line path C₁ is
9
(Type an integer or a simplified fraction.)
(0, 0, 0)
9
(1, 1, 1)
C₁
(1, 1, 0)
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