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b) Find the line integrals of F(x, y, z) = 1+x² (0, 0, 0) to (1, 1, 1) over each of the following paths: 1. The straight line r(t) = ti + tj + tk with 0 ≤ t ≤ 1. 2. The curve r(t) = ti + t²j + tªk with 0 ≤ t ≤ 1. and G(x, y, z) = xyi+yzj+xzk from 3. The path consisting of the straight line segment from (0,0,0) to (1, 1,0) followed by the straight line segment from (1, 1,0) to (1, 1, 1).

b) Find the line integrals of F(x, y, z) = 1+x² (0, 0, 0) to (1, 1, 1) over each of the following paths: 1. The straight line r(t) = ti + tj + tk with 0 ≤ t ≤ 1. 2. The curve r(t) = ti + t²j + tªk with 0 ≤ t ≤ 1. and G(x, y, z) = xyi+yzj+xzk from 3. The path consisting of the straight line segment from (0,0,0) to (1, 1,0) followed by the straight line segment from (1, 1,0) to (1, 1, 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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b) Find the line integrals of F(x, y, z) = 1+x² (0, 0, 0) to (1, 1, 1) over each of the following paths: 1. The straight line r(t) = ti + tj + tk with 0 ≤ t ≤ 1. 2. The curve r(t) = ti + t²j + tªk with 0 ≤ t ≤ 1. 3. The path consisting of the straight line segment from (0,0,0) to (1, 1,0) followed by the straight line segment from (1, 1,0) to (1, 1, 1). and G(x, y, z) = xyi+yzj+xzk from
Transcribed Image Text:b) Find the line integrals of F(x, y, z) = 1+x² (0, 0, 0) to (1, 1, 1) over each of the following paths: 1. The straight line r(t) = ti + tj + tk with 0 ≤ t ≤ 1. 2. The curve r(t) = ti + t²j + tªk with 0 ≤ t ≤ 1. 3. The path consisting of the straight line segment from (0,0,0) to (1, 1,0) followed by the straight line segment from (1, 1,0) to (1, 1, 1). and G(x, y, z) = xyi+yzj+xzk from
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