Math Help - integral limits, i dont understand

1. integral limits, i dont understand

heres a quick overview of my problem for a triple integral i have:

(((_v where bracket is integral sign lol.

where V is the region bounded by the planes x+y+z=a, a>0, x=0, z=0.

my notes say the limits are 0<x<a ,a-x<y<a , a-(x-y)<z<0 for dzdydx.

if i rearrange x+y+z=a i can never come up with the limits i have written down or have a clue how to... how do i get the limits! thanks so much.

2. a-(x-y)<z<0
the z limits should be $0.

Does your book say what you posted?

EDIT: Also, can you post the question?

3. first you must know how to sketch the graph
x+y+z=a
to graph a curve like this first put x or y or z zero lats put z=0

x+y=a now draw this

do the same thing set y to zero and draw z+x=a ...
you will get

now to determine the integral limits

as you can see z values change from 0 to a-x-y this for z
now after you determine limits for a variable now return to the x-y graph
you can see that y values change from 0 to a-x

and finally you can see that x values change from 0 to a
thats all

now
$\int_{0}^{a}\int_{0}^{a-x}\int_{0}^{a-y-z} dzdydx$