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Math Help - Volume of Bounded region

  1. #1
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    Volume of Bounded region

    Hey guys. I'm stuck on a problem for my calc class.
    Let D be the region bounded by the paraboloids z = 2 - x^2 - y^2 and z = 2x^2 + y^2. Find the volume of the region D using an iterated integral.

    I have been trying all night to come up with the limits of integration and the general set up, and I am at a loss.

    So far I have tried to solve by subbing z for itself:
    2 - x^2 - y^2 = 2x^2 + y^2
    but this does not leave a clean answer to transform into spherical.
    you're left with:
    3x^2 + 2y^2 = 2, and I can't see any way to get this into a nice x^2 + y^2 = r^2 format.
    We have a test coming up and my professor said a problem like this would be on it. Any help would be greatly appreciated.
    Last edited by moderata; November 22nd 2010 at 12:39 AM. Reason: added Mathtext to clean up the text structure
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  2. #2
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    even just using (per Allan Cuz's notes): 2 - x^2 - y^2 = 2 - r^2 and 2x^2 + y^2 = 2r^2 you still end up with a weird result: 3r^2 = 2

    I am just totally lost by the integral here. I am sure it will be a triple integral, but I have no idea what to do.
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