The area between $x = y^2$ and $x = 4$ is divided into two equal parts by the line $x = a$, find the value of $a$.

Question

$\begin{array}{1 1} \large\frac{2}{3} \\ \large\frac{4}{3} \\ \large\frac{1}{3} \\ \large\frac{2}{5} \end{array}$