$$\int_{-1}^1\int_{1+x}^1\cos(x+y)e^{(y-x)}\,dy\,dx $$
I suppose the region is this:
$D=\{ (x,y) \in \Bbb R^2 \mid 1+x \le y \le 1$ $ \&$ $ -1\le x \le 1 \}$
But I am not able to understand the region as $x \gt 0 $ and $ 1+x \le y \le 1$ , this is not making sense.
If possible please explain the region graphically.
Edit:
As in comments , i understood the above question.
Now i want to compute the integral using transformation $x +y = u$ and $y-x = v$.
So what is the corresponding region in $uv$ plane.
Please provide the solution to this integral using the transformation.