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Homework Help: Triple Integral with Spherical Coordinates

  1. Apr 21, 2010 #1
    1. The problem statement, all variables and given/known data
    Evaluate [tex]\int\int\int[/tex] 1/[tex]\sqrt{x^{2}+y^{2}+z^{2}+3}[/tex] over boundary B, where B is the ball of radius 2 centered at the origin.


    2. Relevant equations
    Using spherical coordinates:
    x=psin[tex]\Phi[/tex]cos[tex]\Theta[/tex]
    y=psin[tex]\Phi[/tex]sin[tex]\Theta[/tex]
    z=pcos[tex]\Phi[/tex]

    Integral limits:
    dp - [0,2]
    d[tex]\Phi[/tex] - [0,[tex]\pi[/tex]]
    d[tex]\Theta[/tex] - [0,2[tex]\pi[/tex]]

    3. The attempt at a solution
    I am just having trouble finding a good substitution for the integrand. When I substitute x,y, and z with the spherical substitutions, I just get a huge jumbled mess that I can't make any sense of.
     
  2. jcsd
  3. Apr 21, 2010 #2
    whoops sorry, the integrand should be
    [tex]\frac{dV}{\sqrt{x^{2}+y^{2}+z^{2}+3}}[/tex]
     
  4. Apr 21, 2010 #3

    gabbagabbahey

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    Homework Helper
    Gold Member

    Show us. And keep in mind that [itex]\sin^2\eta+\cos^2\eta=1[/itex].
     
  5. Apr 21, 2010 #4
    lol even trying to type that out is a huge jumbled mess in itself. i understand the property you gave me, it's just that i am not able to factor out enough terms such that i leave that identity intact.
     
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