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Find the line integrals of F = 2yi + 4xj + 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+t²k, 0st≤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) ∙y

Find the line integrals of F = 2yi + 4xj + 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+t²k, 0st≤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) ∙y

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 integrals of F = 2yi + 4xj + 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+t²k, 0st≤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) ∙y
Transcribed Image Text:Find the line integrals of F = 2yi + 4xj + 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+t²k, 0st≤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) ∙y
2 Evaluate xy dx + (x + y)dy along the curve y = x² from (-2,4) to (1,1). с
Transcribed Image Text:2 Evaluate xy dx + (x + y)dy along the curve y = x² from (-2,4) to (1,1). с
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