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Triple integral of solid

  1. Jul 7, 2011 #1
    Find the volume of the solid that lies under the paraboloid z = x^2 + y^2, above xy plane,
    and inside the cylinder x^2 + y^2 = 2y

    First, i try to find the range..
    i transfer it to cylindrical coordinates..

    i don't know how to find r
    i know that phi is from 0 to 2pi because it's paraboloid right?
    how am i going to eliminate y? because, y cannot exist in the cylindrical coordinate..
  2. jcsd
  3. Jul 7, 2011 #2


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    the outer r limit will be the cylinder, the inner r limit the parabliod, express the inner limit as r(z)

    the xy plane means the lower limit for z will be z=0

    phi will be from 0 to 2pi, as there is nothing in the problem to limit the angular range, so you must integrate over the whole range
  4. Jul 7, 2011 #3


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    don't forget the jacobian in the integral either
  5. Jul 7, 2011 #4
    got it!! thank u very much!! =)
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