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

  1. Nov 16, 2009 #1
    1. The problem statement, all variables and given/known data
    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.


    2. Relevant equations

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



    3. 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.
     
    Last edited: Nov 16, 2009
  2. jcsd
  3. Nov 16, 2009 #2

    LCKurtz

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