Setting Up Triple Integral for Region Bounded by x=y^2, z=0, x+z=1

[stratusfactio]

Homework Statement

Set up the triple integral for the region bounded by:

$$x=y^2, z=0, x+z=1$$

Homework Equations

The Attempt at a Solution

$$y= ±sqrt(x); z=0 & z=x+1$$
I'm just lost on how to find the x integral. I know the dz integral goes from $$z=0 to z=x+1$$, and I know the dy integral goes from $$y=-sqrt{x} to +sqrt{x}$$. I also know if we set 0=x+1, we get x=1, but how do I find the remaining limit of integration?

 

[I like Serena]

Hi stratusfactio!

Your maximum z is a little off, it should be 1-x.

As for x, what's wrong with 0 to 1?
(I suggest you try to make a drawing.)