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Find the line integral of F= (9x² - 6x) i+ 6z j+ k from (0,0,0) to (1,1,1) over each of the following paths in the accompanying figure. C₁: r(t)=ti+tj+tk, 0sts1 ». C₂: r(t)=ti+t²j+t²k, Osts1 : C3UC4: the path 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) X (0,0,0) C₁ (1,1,1) C4 (1,1,0)

Find the line integral of F= (9x² - 6x) i+ 6z j+ k from (0,0,0) to (1,1,1) over each of the following paths in the accompanying figure. C₁: r(t)=ti+tj+tk, 0sts1 ». C₂: r(t)=ti+t²j+t²k, Osts1 : C3UC4: the path 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) X (0,0,0) C₁ (1,1,1) C4 (1,1,0)

Advanced Engineering Mathematics
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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Find the line integral of F = (9x² − 6x) i + 6z j+ k from (0,0,0) to (1,1,1) over each of the following paths in the accompanying figure. a. C₁: r(t)=ti+tj+tk, Osts1 b. C₂: r(t)=ti+t²j+t²k, Osts1 c. C3UC4: the path 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) 8 (0,0,0) C₁ (1,1,1) (1,1,0)
Transcribed Image Text:Find the line integral of F = (9x² − 6x) i + 6z j+ k from (0,0,0) to (1,1,1) over each of the following paths in the accompanying figure. a. C₁: r(t)=ti+tj+tk, Osts1 b. C₂: r(t)=ti+t²j+t²k, Osts1 c. C3UC4: the path 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) 8 (0,0,0) C₁ (1,1,1) (1,1,0)
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