Find the line integrals of F = 4yi + xj + 2zk 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, Osts 1 b. The curved path C₂: r(t) = ti + t²j+t4k, 0sts 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) CA (1, 1,0) a. The line integral of F over the straight-line path C₁ is (Type an integer or a simplified fraction.) b. The line integral of F over the curved path C₂ is (Type an integer or a simplified fraction.) c. The line integral of F over the path C3 UC4 is (Type an integer or a simplified fraction.)
Find the line integrals of F = 4yi + xj + 2zk 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, Osts 1 b. The curved path C₂: r(t) = ti + t²j+t4k, 0sts 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) CA (1, 1,0) a. The line integral of F over the straight-line path C₁ is (Type an integer or a simplified fraction.) b. The line integral of F over the curved path C₂ is (Type an integer or a simplified fraction.) c. The line integral of F over the path C3 UC4 is (Type an integer or a simplified fraction.)
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 integrals of F = 4yi + xj + 2zk 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, Osts 1
b. The curved path C₂: r(t) = ti + t²j+t4k, 0sts 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)
C₁
(1, 1,0)
a. The line integral of F over the straight-line path
C₁ is
(Type an integer or a simplified fraction.)
b. The line integral of F over the curved path C₂
is
(Type an integer or a simplified fraction.)
c. The line integral of F over the path C3 UC4 is
(Type an integer or a simplified fraction.)
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