The question:

"Let A be the region defined by the inequalities:

x > 0, y > 0, z > 0,

1 ≤ xyz ≤ 8,

x ≤ y ≤ 2x,

x ≤ z.

(a) Find the volume of A.

(b) Find the integral of e^(xyz) over A."

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What I've tried:

I'm not even sure what the right substitution to use here is. I was thinking u = xyz, v = y/x, w = z/x which would give us

1 ≤ u ≤ 8,

1 ≤ v ≤ 2

1 ≤ w

and I was thinking that we could compute the Jacobian from this (though it would be quite messy...) and then use these intervals as the bounds for u,v,w when we integrate in the order du dv dw.