4.(10 points) (DO NOT INTEGRATE) Using Stokes' Theorem with an appropriate choice of Upper $S$, rewrite the given line integral $\oint_C \mathbf{F} d\mathbf{r}$ as an area integral over the appropriate region of the $xy$-plane. Assume that Upper $C$ has a counterclockwise orientation when viewed from above.
$\mathbf{F} = (5y, -2z, x)$
$C$ is the circle $x^2 + y^2 = 7$ in the plane $z = 0$.
$\oint_C \mathbf{F} d\mathbf{r} = \iint_S$ _________ $dS$
