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Triple integral w/ spherical subsitution

  1. Aug 9, 2011 #1
    1. The problem statement, all variables and given/known data
    f(x) is a differentiable function let
    [itex]F(t)= \int\int\int_{x^2+y^2+z^2\leq t^2} f(x^2+y^2+z^2) dx dy dz [/itex]

    compute F[itex]^{'}[/itex](t)

    2. Relevant equations

    x=p sin [itex]\phi[/itex] cos[itex]\theta[/itex]
    y= p sin [itex]\phi[/itex] sin[itex]\theta[/itex]
    z= p cos [itex]\phi[/itex]

    spherical bounds 0<p<t 0<[itex]\phi[/itex]<[itex]\Pi[/itex] 0<[itex]\theta[/itex] < 2[itex]\Pi[/itex]

    p^2 sin[itex]\phi[/itex] = jacobian determinant

    3. The attempt at a solution

    carried through the substitution [itex]\int\int\int f(p^2) p^2 sin \phi dp d\phi d\theta[/itex]

    dont know how to evaluate [itex]\int[/itex]f(p^2) sin[itex]\phi[/itex] d[itex]\phi[/itex]???
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 9, 2011 #2

    Pengwuino

    User Avatar
    Gold Member

    Be careful about putting those repeated copies of the template in your questions.

    The remaining integral is trivial. Your function is independent of [itex]\phi[/itex] so the [itex]\phi[/itex] integration is trivial; it's just the integral of [itex]sin(\phi)[/itex]
     
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