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.)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 18EQ
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