Let $\gamma$ be the path in $\Bbb{R^3}$ parametrized as x$(t)=(cos(2t), sin(t), sin(2t))$ for $t \in [0,2\pi]$.
Let A be the vector field with components $(x,-y^2,0)$, where $(x,y,z)$ are Cartesian coordinates in $\Bbb{R^3}$. Evaluate
$\displaystyle \int_{\gamma}$ A$\cdot$ ds
I think I'm meant to find ||x'(t)|| which I'm getting as $\sqrt{4sin^{2}2t +cos^{2}t +4cos^{2}2t}$ which I'm not sure is even right or if am just meant to find x'(t)...?
Any help is appreciated