# Triple Integral - How to set up limits?

1. Nov 2, 2012

### jazzhands1

1. The problem statement, all variables and given/known data

Find the limits of this region of integration, and write all possible equivalent iterated integrals given combinations of dz, dy, and dx.

2. Relevant equations
none that are really 'equations'?

3. The attempt at a solution
In particular, I'm having trouble with the order dy dz dx, as in:
∫∫∫ dy dz dx

I can get -1 and -√z for the bottom and top limits of the first integral (∫ dy) but I'm having a harder time finding the limits for ∫∫ dz dx in the z-x plane. I get 0 and y^2 for the top and bottom limits of that ∫dz, which shouldn't be right since it both should be functions of (x) and not of (y).

I'd appreciate a pointer or hint. Thanks!

2. Nov 2, 2012

### clamtrox

First thing you note is that x is completely independent of y and z.

Let's then say y can be anywhere between zero and one. Which values of z are allowed for each y? This gives you the limits for the z-integral.

3. Nov 3, 2012

### jazzhands1

Got it, thanks a bunch! =)