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5. Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (1, 0, 0) to (1, 0, 1). a. The line segment x = 1, y = 0,0 ≤z ≤ 1 b. The helix r(t) = (cost)i + (sin t)j + ()k; 0 ≤ t ≤ 2π C. The x-axis from (1, 0, 0) to (0, 0, 0) followed by the parabola z = y², y = 0 from (0, 0, 0) to (1, 0, 1)

5. Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (1, 0, 0) to (1, 0, 1). a. The line segment x = 1, y = 0,0 ≤z ≤ 1 b. The helix r(t) = (cost)i + (sin t)j + ()k; 0 ≤ t ≤ 2π C. The x-axis from (1, 0, 0) to (0, 0, 0) followed by the parabola z = y², y = 0 from (0, 0, 0) to (1, 0, 1)

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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5. Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (1, 0, 0) to (1, 0, 1). a. The line segment x = 1, y = 0,0 ≤ z≤ 1 b. The helix r(t) = (cost)i + (sin t)j + (1) k; 0 ≤ t ≤ 2π C. The x-axis from (1, 0, 0) to (0, 0, 0) followed by the parabola z = y², y = 0 from (0, 0, 0)to (1, 0, 1)
Transcribed Image Text:5. Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (1, 0, 0) to (1, 0, 1). a. The line segment x = 1, y = 0,0 ≤ z≤ 1 b. The helix r(t) = (cost)i + (sin t)j + (1) k; 0 ≤ t ≤ 2π C. The x-axis from (1, 0, 0) to (0, 0, 0) followed by the parabola z = y², y = 0 from (0, 0, 0)to (1, 0, 1)
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