It looks simple, but I'm having a bit of difficulty with trying to obtain the proper change of coordinates.
Evaluate the following integral
with region R in the first quadrant bounded by $-1\le y-x\le 1$ and $1\le x^2+y^2 \le 4$
I've tried $u=x^2+y^2$ and $v=y-x$, but I can't seem to express $x+y$ in terms of $u$ and $v$. Is it possible to express $x+y$ in terms of $u$ and $v$ with the above substitutions? Or do we need another change of variables?
What other change of coordinates is possible to approach this problem? Based on what region $R$ looks like, I don't think polar coordinates would work for this even though there is an $x^2+y^2$ term (though I could be mistaken).