Find the line integrals of F =2yi+3xj + 4zk from (0,0,0) to (1,1,1) over each of the following paths. a. The line integral of F over the straight-line path C, is. a. The straight-line path C,: r(t) = ti + tj + tk, 0sts1 (Type an integer or a simplified fraction.) b. The curved path C2: r(t) = ti + tʻj+t°k, 0sts1 c. The path C3UC, 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) b. The line integral of F over the curved path C, is. (Type an integer or a simplified fraction.) c. The line integral of F over the path C3UC, is (0, 0, 0) (1, 1, 1) (Type an integer or a simplified fraction.) (1, 1, 0)
Find the line integrals of F =2yi+3xj + 4zk from (0,0,0) to (1,1,1) over each of the following paths. a. The line integral of F over the straight-line path C, is. a. The straight-line path C,: r(t) = ti + tj + tk, 0sts1 (Type an integer or a simplified fraction.) b. The curved path C2: r(t) = ti + tʻj+t°k, 0sts1 c. The path C3UC, 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) b. The line integral of F over the curved path C, is. (Type an integer or a simplified fraction.) c. The line integral of F over the path C3UC, is (0, 0, 0) (1, 1, 1) (Type an integer or a simplified fraction.) (1, 1, 0)
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 = 2yi+3xj + 4zk from (0,0,0) to (1,1,1) over each of the following paths.
a. The line integral of F over the straight-line path C, is.
a. The straight-line path C,: r(t) = ti + tj + tk, 0sts1
(Type an integer or a simplified fraction.)
b. The curved path C2: r(t) = ti + tj+t°k, 0sts1
c. The path C3UC, 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)
b. The line integral of F over the curved path C, is
(Type an integer or a simplified fraction.)
c. The line integral of F over the path C3UC, is
(0, 0, 0)
e(1, 1. 1)
(Type an integer or a simplified fraction.)
(1, 1,0)
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