# Does triple integrals have to have a specific interval?

1. Aug 24, 2013

### Ayham

I hope this makes my question clear...
suppose we have a triple integral of dzdydx for [0<x<1 , sqt(x)<y<1 , 0<z<1-y] and from the sketch we can see that 0<y<1 and 0<z<1...
my question is this, if we change the integration to dzdxdy we get [0<x<y^2 , 0<y<1 , 0<z<1-y], is that the only way? or can we make the x like 0<x<1 or y^2<x<1 and still get the same answer?

I hope i made my question correctly clear, and sorry if i put this in the wrong place :)
help appreciated ^_^

2. Aug 24, 2013

### Electric Red

Next time it is better to put things in LaTeX, read the FAQ for that, that would be a lot easier te read. But, to answer your question, as long as you define the boundaries of your integrals correct, you should get the same answer.
So if you get an different answer after changing from dxdydz to dydxdz, you probably messed up your boundaries.
(with boundaries I mean things like 0<x<1)

3. Aug 24, 2013

### tiny-tim

Hi Ayham!
yes, you integrate wrt z first, keeping x and y constant

then you integrate wrt y, keeping x constant

then you integrate wrt x, and there aren't any constants left!
if you integrate wrt x second (instead of y), then you must keep y constant, you can't ignore it, it's still there …

0 < x < y2