I have this function
$ f(x,y,z) = x + y $
and I want to find
$ \iint f(x,y,z) dS $
Where S is the first octant part of the plane
$ x + y + z =1 $
Now, I know the method, and have paramatrized like this
$ z = 1 - x - y,\, x = x,\, y = y. $ However, I thought the bounds of integration for x and y were between 0 and 1, but doing this gives me an answer of $3^{0.5}$, when the answer is $(3^{1/2})/3$, implying that the bounds that my textbook is using are different.
What are they?