Integration over a set

Let $\Omega=\{(x,y)\in \mathbb{R}^2:0<x<y<2x<2\}$

Now I've got to integrate$\int_{\Omega}{ydxdy}$ over $\Omega$.Something is wrong with my integral because I get the false result.I've calculated $\int_{0}^{2}[\int_{x}^{2x}{y}dy]dx$ with result 4. Have I chosen a wrong integral?