# Triple integral question

I= [∫(0 to 1) ∫(0 to 2z) ∫(z to 1) dx dy dz] + [ ∫(0 to 1) ∫(2z to 1+z) ∫(y-z to 1) dx dy dz]

1) evaluate
2) use order dy dx dz, along with the new bounds

my attempt for 1) got me an answer of -7/6

for part 2) i'm having trouble getting the correct bounds. the bounds from my attempt are
D1 = {(x, y)|0 ≤ x ≤ 2z, z ≤ y ≤ 1}
D2 = {(x, y)|2z ≤ x ≤ 1+z, x+z ≤ y ≤ 1 }

i can do integration easily, and am nearly finished with this question, but its the bounds that are prohibiting me from progressing any further.

please any help would be good. i tried trying 2d graphs and so forth already...

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HallsofIvy
$$\int_{z=0}^1\int_{x= z}^1\int_{y= 0}^{2z} dy dx dz$$
$$\int_{z=0}^1\int_{x= 1}^z\int_{y= 0}^{x+ z} dy dx dz$$.