Evaluate $\int\int_R \frac{y.e^{2y}}{\sqrt{(1-x)(x-y)}}dx.dy$ where $R$ is the region of the triangle whose vertices are $(0,0), (1,0)$ and $(1,1)$.
So far, I have managed to figure out that this can be written as: $$\int_0 ^1\int_o ^x\frac{y.e^{2y}}{\sqrt{(1-x)(x-y)}}dy.dx$$
$$\int_0 ^1\frac{dx}{\sqrt{1-x}}\int_o ^x\frac{y.e^{2y}}{\sqrt{x-y}}dy$$
Please tell me how do I proceed from here