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Help with volume

  1. Nov 28, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the volume between the two surfaces

    z = 2x^2 + y^2

    z = 4 - y^2

    2. Relevant equations

    3. The attempt at a solution

    Ok so i found out that the surfaces intersect at a circle. When i solved i got

    x^2 + y^2 = 2, so the circle has a radius of sqrt 2.

    So these are the bounds i got. X goes from - sqrt 2 to sqrt 2, y goes from - sqrt 2-x^2 to sqrt 2-x^2 and z goes from 4-y^2 to 2x^2 + y^2.

    Is that right? If so, what is the equation I am integrating? Is it always integrating 1 dx dy dz?
  2. jcsd
  3. Nov 28, 2011 #2


    User Avatar
    Science Advisor

    That would certainly work. And what would be the bounds on the z-integral?

    (Also, because of the circular symmetry, I would be inclined to use cylindrical coordinates- but you certainly can do it the way you suggest.)
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