Probability on parabolic domain

Let $(X, Y)$ be a random vector having the joint probability density function $$f(x, y)=\begin{cases} \alpha |x|, & \text{if }x^2 \le y \le 2x^2, -1 \le x \le 1, \ 0, & \text{otherwise,} \end{cases}$$ where $\alpha$ is a positive constant. Then, $P(X > Y)$ equals