I'm trying to figure out how to switch the order of integration for this problem. I'm given the region (I don't know how to use latex, maybe someone can clean this up for me?)
$z$ from $0$ to $x+y$
$y$ from $0$ to $1-x$
$x$ from $0$ to $1$
That was for the integral $dz\;dy\;dx$ and I have to change it to $dy\;dx\;dz$. I think maybe I drew out the region wrong and that's why I can't figure this out. The one I drew looks like a right triangle. In the first octant The $x$ axis from 0 to 1 and the hypotenuse of the triangle is the line $1-x$ then it goes out in $y$ from 0 to 1 (I can upload the picture if it helps). I don't think I'm taking the $x+y$ part into account anywhere? The new integral I came up with is
$y$ from $0$ to $1$
$x$ from $0$ to $1-y$
$z$ from $0$ to $1$