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Math Help - Paraboliod Help

  1. #1
    Junior Member
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    Feb 2010
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    Paraboliod Help

    I'm supposed to find the volume of the solid enclosed by z=x^2+3y^2 and the planes x=0, y=1, y=x and z=0. I'm not even sure what that looks like though, hence I don't know what the limits of integration are, or even what to integrate. Can someone help me get started?
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  2. #2
    Junior Member
    Joined
    Jan 2010
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    In order to be able to solve these kinds of volume questions, you must learn to draw or at least visualize the area you are finding. I will help you here, but eventually you're going to have to be able to do it yourself.

    First of all the z=0 bound is unnecessary as this elliptic paraboloids vertex is at (0,0,0). z is bounded above by your function. y goes from x to 1, and x goes from 0 to infinity.

    \displaystyle\int_0^\infty\displaystyle\int_x^1 x^2+3y^2\,dy\,dx


    EDIT: These bounds could also describe an area where y goes from x to 1 and x goes from -1 to 0, which may be what your professor is looking for since its supposed to be an enclosed volume
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