Calculate the line integral of the vector field $F = \langle y, x, x^2 + y^2 \rangle$ around the boundary curve, the curl of the vector field, and surface integral of the curl of the vector field.
The surface $\square$ is the upper hemisphere
$x^2 + y^2 + z^2 = 16, z \ge 0$
oriented with an upward-pointing normal.
(Use symbolic notation and fractions where needed.)
$\oint_C F \cdot dr = 0$
$\text{curl}(F) = 2yi - 2xj$
$\iint_S \text{curl}(F) \cdot dS = $
