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?