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Homework Help: Triple integral volume of solid (set up)

  1. Nov 10, 2012 #1
    1. The problem statement, all variables and given/known data
    I need help setting this integral up in spherical coordinates, the region above the xyplane, inside the sphere x^2+y^2+z^2=2 and outside the cylinder x^2+y^2=2

    3. The attempt at a solution

    [itex]\int^{2\pi}_{0}[/itex] [itex]\int^{\pi/2}_{\pi/4}[/itex] [itex]\int^{\sqrt{2}}_{0}[/itex] [itex]\rho^{2}[/itex]sin[itex]\phi[/itex]d[itex]\rho[/itex]d[itex]\theta[/itex]d[itex]\theta[/itex] -[itex]\int^{2\pi}_{0}[/itex] [itex]\int^{\pi/4}_{0}[/itex] [itex]\int^{1/sin\phi}_{0}[/itex] [itex]\rho^{2}[/itex]sin[itex]\phi[/itex]d[itex]\rho[/itex]d[itex]\phi[/itex]d[itex]\theta[/itex]

    is this correct?
  2. jcsd
  3. Nov 10, 2012 #2
    cylinder is x^2+y^2=1 oops, and on first integrand its drho,dphi,dtheta.
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