Find the line integrals of F from (0, 0, 0) to (1, 1, 1) over each of the following paths in the accompanying figure.

a. The straight-line path C₁: r(t) = ti + tj + tk, 0 ≤ t ≤ 1

b. The curved path C₂: r(t) = ti + t²j + t⁴k, 0 ≤ t ≤ 1

c. The path C₃ ∪ C₄ 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)

F = (3x² - 3x)i + 3zj + k

Transcribed Image Text:

X (0, 0, 0) Ş NE C₁(1, 1, 1) C3 CA (1, 1, 0) y