Find the line integrals of F from (0, 0, 0) to (1, 1, 1) over each of

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


image


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 = xyi + yzj + xzk

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Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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