Chapter 14, Problem 27RE

Evaluating line integrals Evaluate the line integral ${\displaystyle {\int }_{C}F\cdot dr}$ for the following vector fields F and curves C in two ways.

a.    By parameterizing C

b.    By using the Fundamental Theorem for line integrals, if possible

27.    F = 〈y, z, –x〉; C: r(t) = 〈cos t, sin t, 4〉, for 0 ≤ t ≤ 2π