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Find the line integral of F= 2√zi-4xj + 3√√yk, 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+tªk, 0≤ts1 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)

Find the line integral of F= 2√zi-4xj + 3√√yk, 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+tªk, 0≤ts1 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)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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find b and c

Find the line integral of F= 2√√/Zi-4xj+ 3√√yk, 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, 0≤t≤ 1 b. The curved path C₂: r(t) = ti+t²j+tªk, 0≤t≤1 c. The path C3UC4 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) 4 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.) (0, 0, 0) C₂₁ (1, 1, 1) C₁ (1, 1, 0)
Transcribed Image Text:Find the line integral of F= 2√√/Zi-4xj+ 3√√yk, 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, 0≤t≤ 1 b. The curved path C₂: r(t) = ti+t²j+tªk, 0≤t≤1 c. The path C3UC4 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) 4 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.) (0, 0, 0) C₂₁ (1, 1, 1) C₁ (1, 1, 0)
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