Volume of 2-sphere using triple integration (rect. cord)

[battlebball]

Homework Statement

Can anyone help me with the volume of a 2-sphere in rect cordinates? I'm having problems with the limits of the triple integral. Ultimately I will need to go beyond the 2-sphere to a 3 and 4 using quadruple and five integrals respectively. Radius at r from 0 vector.

Homework Equations

x^2+y^2+z^2+u^2=r^2

The Attempt at a Solution

So I assume the eq. is x^2+y^2+z^2=r^2
If I have x as my first and dependent interval would the limit be from -r to r?

2nd limit: -(r^2-x^2)^1/2 to (r^2-x^2)^1/2?

3rd limit: -(r^2-x^2-y^2)^1/2 to (r^2-x^2-y^2)^1/2

so then if I wanted to go to a 3 etc:

4th limit: -(r^2-x^2-y^2-u^2)^1/2 to (r^2-x^2-y^2-u^2)^1/2??I appreciate the help, I've been sick from class a few days and need help with the notes from class.

 

[LCKurtz]

So I assume the eq. is x^2+y^2+z^2=r^2
If I have x as my first and dependent interval would the limit be from -r to r?

2nd limit: -(r^2-x^2)^1/2 to (r^2-x^2)^1/2?

3rd limit: -(r^2-x^2-y^2)^1/2 to (r^2-x^2-y^2)^1/2

If by 1st, 2nd, and 3rd limits, you mean the outer, middle, and inner limits on a dzdydx integral, then yes, those look OK.