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Find the line integrals of F = yi + 3xj + zk 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+t²k, osts 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) * (1, 1,0) a. The line integral of F over the straight-line path C, is (Type an integer or a simplified fraction.)

Find the line integrals of F = yi + 3xj + zk 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+t²k, osts 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) * (1, 1,0) a. The line integral of F over the straight-line path C, is (Type an integer or a simplified fraction.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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Please find part a b and c

Find the line integrals of F = yi + 3xj + zk 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, 0st≤1 b. The curved path C₂: r(t) = ti+t²j+t4k, Osts 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.)
Transcribed Image Text:Find the line integrals of F = yi + 3xj + zk 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, 0st≤1 b. The curved path C₂: r(t) = ti+t²j+t4k, Osts 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.)
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