[tex] \oint_{c}(2 + x {}^{2} y + z) \: ds \\ \\ \oint_{c}f(x , y,z) \: ds = \oint _{c}f(t). \left| \frac{dr}{dt} \right| dt[/tex]

[tex]r(t) =( \cos(t), \: \sin(t), \: 0,2t) \\ \frac{dr(t)}{dt} = ( - \sin(t), \: \cos(t), \: 0,2) \\ \left | \frac{dr(t)}{dt} \right| = \sqrt{( - \sin(t)) {}^{2} + (\cos(t)) {}^{2} +(0,2) {}^{2} } \\ \left | \frac{dr(t)}{dt} \right| = \sqrt{ \sin {}^{2}(t) + \cos {}^{2} (t) + 0,04} \\ \left | \frac{dr(t)}{dt} \right| = \sqrt{1 +0,04} \\ \left | \frac{dr(t)}{dt} \right| = 1,019[/tex]

[tex] \int_{0}^{2\pi} (2 + \cos {}^{2} (t). \sin(t) +0,2t).(1,019)dt \\ \\ \int_{0}^{2\pi}( 2,038 + 1,019 \cos {}^{2} (t). \sin(t) + 0,2038t)dt \\ \\ \left(2,038t - \frac{1,019 \cos {}^{3} (t)}{3} + \frac{0,2038t {}^{2} }{2} \right) _{0} ^{2\pi} \\ \\ \left(2,038 .2\pi - \frac{1,019 \cos {}^{3} (2\pi)}{3} + \frac{0,2038.(2\pi){}^{2} }{2} \right) =\boxed{ \boxed { 16,48}}[/tex]

Pelo resultado, imagino que seja o item a)