Suppose $\vec{F}(x,y) = -y \sin(x) \vec{i} + \cos(x) \vec{j}$.

(a) Find a vector parametric equation for the parabola $y = x^2$ from the origin to the point $\left(3,9\right)$ using $t$ as a parameter.
$\vec{r}(t) =$

(b) Find the line integral of $\vec{F}$ along the parabola $y = x^2$ from the origin to $\left(3,9\right)$.