# Math Help - Triplle integral

1. ## Triplle integral

I have a region W which is a rectangular box with corners at : (0,0,0), (a,0,0), (0,b,0) and (0,0,c). the function of this is e^(-x -y - z) I am suppose to find the triple integral of the function over the region W.

I am having trouble with this. I have the outermost integral from 0 to c the middle one from 0 to b and then the inner from 0 to a with the order dx dy dz. I am not getting close to the answer that I am suppose to. It could be just because this is the very first triple I have tried to solve but,..... Thanks to all who help on this forum. Frostking

2. Originally Posted by Frostking
I have a region W which is a rectangular box with corners at : (0,0,0), (a,0,0), (0,b,0) and (0,0,c). the function of this is e^(-x -y - z) I am suppose to find the triple integral of the function over the region W.

I am having trouble with this. I have the outermost integral from 0 to c the middle one from 0 to b and then the inner from 0 to a with the order dx dy dz. I am not getting close to the answer that I am suppose to. It could be just because this is the very first triple I have tried to solve but,..... Thanks to all who help on this forum. Frostking
Notice that $e^{-x-y-z} = e^{-x}e^{-y}e^{-z}$.
Therefore, $\iiint_W f = \left( \int_0^a e^{-x} dx\right) \left( \int_0^b e^{-y}dy \right) \left( \int_0^c e^{-z}dz \right)$.

The reason why this is possible is because the function is "seperable" i.e. $f(x,y,z)$ can be factored as $g(x)h(y)k(z)$.