I'm trying to set up this triple integral with the following bounds: x=0, y=0, z=0, x+y=1, z=x+y. Now I first computed the volume to be 1/3 with a double integral and then what I've been doing is setting what I think are the right bounds for the triple integral and integrating f(x,y,z)=1 to see if that matches the volume. I also think that because of symmetry ∫∫∫xdxdydz = ∫∫∫ydxdydz so I have been checking the correctness of my bounds that way as well. Finally I have come up with bounds that check out both ways but they seem too simple to be correct, if you could help verify them or provide the correct ones if they are wrong that would be excellent. Here they are from outer to inner: z=0 to z=1, y=0 to y=z, x=0 to x=z. Thanks.