Evaluate $\oint_C(y^3+\cos x)dx + (\sin y+z^2)dy+xdz$
where C is oriented by the tangent vector given by the parametrization r.
$r:[0,2\pi]\rightarrow R^3,t\rightarrow (\cos t,\sin t, \sin 2t)$
i am having trouble with this because I don't know how to get the boundaries or I get really weird integrals which i believe aren't solvable like $\cos( \cos (t))$. I thought I could use Stokes theorem but then i get to a integral which I also don't know how to solve which is
$\iint_S (2z\hat{x}+(3y^2-1)\hat{y}-3y^2\hat{z}) dS$
can someone help me?
Hint: the projection of the curve on the $XY$ plane is the unit circle and as $\sin 2t = 2\sin t\cos t$, the curve $\subset$ in the surface $z = 2xy$. Can you continue?