How Do You Set Up Triple Integrals for Bounded Regions in Calculus?

[cookiesyum]

Homework Statement

Consider a region in the first octant bounded by z=1-x^2 and y = 1-x. Write the integral in the order dx dy dz and dx dz dy.

Homework Equations

The Attempt at a Solution

For the first one:

z varies from 0 to 1.
y (in terms of z) varies from...1 to 1??
x (in terms of z and y) varies from -sqrt(1-z) to sqrt(1-z)-y??

For the second one:

y varies from 0 to 1.
z (in terms of y) varies from 1 to 1?
x (in terms of y and z) varies from -sqrt(1-z) to sqrt(1-z)-y??

I'm not sure what to do about the y as it is always at 1 in terms of x.

 

[Billy Bob]

Neither one is correct. You have to draw the picture to visualize this. Once you have drawn the picture, look at it from the usual orientation, but also look at it directly from the "front" (i.e., look toward the yz plane).