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Evaluate the triple integral

  1. Aug 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Evaluate the triple integral where E is the solid bounded by the cylinder y^2+ z^2 = 576 and the planes x = 0, y = 4 x and z =0 in the first octant.


    2. Relevant equations



    3. The attempt at a solution
    I figure that by solving for z I can get the bounds, so between 0 to sqrt(576-y^2) would be the z upper and lower bounds. X bounds would be between 0 and 24? And I am not sure about y.
     
  2. jcsd
  3. Aug 3, 2009 #2

    HallsofIvy

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    I presume you mean "the triple integral for the volume"- i.e. just integrate dV= dxdydz over that region. Otherwise you haven't said what it is you want to integrate! I think, because of the spherical symmetry here, using spherical coordinates would be best. Obviously [itex]\rho[/itex] will go from 0 to [itex]\sqrt{576}= 24[/itex], [itex]\phi[/itex] from 0 to [itex]\pi/2[/itex] and, since y= 4x has slope 4, [itex]\theta[/itex] will go from 0 to arctan(4).
     
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