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$[20$ points$]$ Evaluate the line integral $in$ Stokes$$ Theorem $to$ evaluate the surface integral

$S$

$F$

$*dS$ for the following vector field and surface. Assume that the normal vector $n$

points $inan$ upward direction.

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$F(x,y,z)=(-y,x,z)$

$Sis$ the part $of$ the paraboloid defined $byr(t)=(cos(t),sin(t),3cos2$

$(t)+sin2$

$(t))$