Answer
$x+y^2\leq4$
Work Step by Step
Since the boundary of the curve is solid, the inequality would be either $x+y^2\geq4$ or $x+y^2\leq4$
Use a test point $(0,0)$ in the shaded region (solution region) to evaluate the the value of the equation, we found $x+y^2=0\lt4$.
Thus we conclude the inequality as $x+y^2\leq4$
