In Exercises 7–12, find the line integrals of F from (0, 0, 0) to (1, 1, 1) over each of the following paths in the accompanying figure. a. The straight-line path C¡: r(t) = ti + tj + tk, 0

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Chapter1: Functions And Models
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In Exercises 7–12, find the line integrals of F from (0, 0, 0) to (1, 1, 1)
over each of the following paths in the accompanying figure.
a. The straight-line path C¡: r(t) = ti + tj + tk, 0<t< 1
b. The curved path C2: r(t) = ti + tj + t*k, 0<t< 1
c. The path C3 U C4 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)
7. F = 3yi + 2xj + 4zk
8. F = [1/(x² + 1) ]j
9. F = Vzi – 2xj + Vyk
10. F = xyi + yzj + xzk
11. F = (3x² – 3x)i + 3zj + k
12. F = (y + z)i + (z + x)j + (x + y)k
(0, 0, 0)
C¡ (1, 1, 1)
C4
C3
х
(1, 1, 0)
Transcribed Image Text:In Exercises 7–12, find the line integrals of F from (0, 0, 0) to (1, 1, 1) over each of the following paths in the accompanying figure. a. The straight-line path C¡: r(t) = ti + tj + tk, 0<t< 1 b. The curved path C2: r(t) = ti + tj + t*k, 0<t< 1 c. The path C3 U C4 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) 7. F = 3yi + 2xj + 4zk 8. F = [1/(x² + 1) ]j 9. F = Vzi – 2xj + Vyk 10. F = xyi + yzj + xzk 11. F = (3x² – 3x)i + 3zj + k 12. F = (y + z)i + (z + x)j + (x + y)k (0, 0, 0) C¡ (1, 1, 1) C4 C3 х (1, 1, 0)
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