Chapter 14.3, Problem 37E

Line integrals of vector fields on closed curves Evaluate ${\displaystyle {\oint }_{C}F\cdot dr}$ for the following vector fields and closed oriented curves C by parameterizing C. If the integral is not zero, give an explanation.

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