I'm having a problem in the following exercise:
Using an appropiate substituion, calculate:
$$\iiint\frac{\sin{(x+y-z)}}{x+2y+z}\,dx\,dy\,dz$$
$1 \leq x+2y+z\leq 2$, $0 \leq x+y-z \leq \frac{\pi}{4}$ and $0 \leq z \leq 1$
Since $z$ is given by the author, is fairly easy to setup for it:
$$\int_0^1\int\int\frac{\sin{(x+y-z)}}{x+2y+z}\,dx\,dy\,dz$$
What about for $x$ and $y$? I know it may be easier if I plot the graph, but how to solve it without using this "shortcut"? Should I put $x$ in function of $y$ and $y$ in function of $z$? If yes, how to do that?