Volume integrals

The function f(x,y,z) = y is defined on the domain:

{(x,y,z) | 0 <= y, x^2+ y^2 + z^2 <= 1}

When finding the integral I need to have upper and lower bounds. So far I have found:

y2 <= 1-x2-z2 <=>
y <= sqrt(1-x2-z2)

I then have:

0 <= y <= sqrt(1-x2-z2)

and can then repeat for z and x:

z <= sqrt(1-x2-y2)
x <= sqrt(1-z2-y2)

But then I still need the lower bounds for z and x or am I approaching the problem in a wrong way?
.

Relevant Pages

  • Re: [Translation] framing of an expression ?
    ... It is common expression in french, and seems to me usefull, ... to avoid to repeat twelve times 'lower and upper bounds'... ... I think I may have seen the phrase "absolutely bounded", ... defined in the most general context wherein upper and lower bounds ...
    (sci.math)
  • Re: fmincon error in planerot (bug?)
    ... when constraining the solution with upper and lower bounds. ... (rest of original post removed for brevity) ... I found I can usually avoid this ...
    (comp.soft-sys.matlab)
  • Re: Creating 2D graphic strip chart with trace wrapping
    ... The dynamic range of some of the data traces is quite large, ... "shoots through" the upper limit, it re-enters from the lower limit. ... somehow possible to reflect the 2D line at the upper and lower bounds, ...
    (comp.graphics.api.opengl)
  • Re: Length & number of radials
    ... handle on upper and lower bounds. ... our elementary physics books. ...
    (rec.radio.amateur.antenna)
  • Re: Series sin(n^2)/n
    ... he also investigated partial products of type ... he gave upper and lower bounds. ... also of intrest to him where questions like these: ...
    (sci.math)