Find the line integral of F= √√zi-2xj + √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+t^k, Osts 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) 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.) x c. The line integral of F over the path C3 UC4 is (Type an integer or a simplified fraction.) (0, 0, 0) C₁

Find the line integral of F= √√zi-2xj + √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+t^k, Osts 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) 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.) x c. The line integral of F over the path C3 UC4 is (Type an integer or a simplified fraction.) (0, 0, 0) C₁

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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