Mean from a quadratic CDF

Let $X$ be a continuous random variable with distribution function $$F(x)=\begin{cases}0,&\text{if }x<0\\ax^{2},&\text{if }0\le x<2\\1,&\text{if }x\ge 2\end{cases},$$ for some real constant $a$. Then, $E(X)$ is equal to