use triple integral to find the volume of tetrahedron enclosed by the coordinat planes "x=o , y=0 , z=0" and the plane 2x+y+z=0
The Attempt at a Solution
I will integrate the constant function f(x,y,z)=1 by the order : dzdydx
the equation will be : z=-2x-y
so the limits for the inner integral will be from 0 to -2x-y
when z=0 ---> y=-2x
so the limits for the middle integral will be from 0 to -2x
THE PROBLEM HERE IS THAT
when z=0,y=0 ---> x=0 .. !
so the limits for the outer integral will be from 0 to 0 .. !
and this means the triple integral will be 0 .. !
so there is no volume ??!