Does triple integrals have to have a specific interval?

[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 ^_^

 

[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)

I hope I answered your question (:

 

[tiny-tim]

Hi Ayham!

suppose we have a triple integral of dzdydx for [0<x<1 , sqt(x)<y<1 , 0<z<1-y]

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!

f 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?

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