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Homework Help: Volume in cylindrical coordinates

  1. Nov 4, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the volume using cylindrical coordinates bounded by:

    x2+y2+z2=2 and

    z = x2+y2

    2. Relevant equations

    Converting to cylindrical coordinates:
    z = √2-r2 and

    z = r2

    3. The attempt at a solution

    I figured z would go from r2 to √2-r2
    r from 0 to √2
    and θ from 0 to 2∏.
    However, when I evaluate the integral I get a negative volume. (And no, I did not forget to multiply by an extra r)

    I have no idea where I've gone wrong.
  2. jcsd
  3. Nov 4, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    What is the x,y equation of the intersection of your two surfaces? Are you sure you copied the problem correctly?
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