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Confused on double integral in polar cords

  1. Feb 25, 2010 #1
    1. The problem statement, all variables and given/known data
    Use polar coordinates to find the volume of the solid enclosed by the hyperboloid -x^2-y^2+z^2=1 and the plane z=2.

    3. The attempt at a solution
    Solving for z of the equation of the hyperboloid I find z = Sqrt(1 + x^2 + y^2). Letting z = 2 to determine the curve of intersection I find that 3 = x^2 + y^2, or r = Sqrt(3). Thus:

    [tex]\int _{0}^{2Pi} \int _{0}^{3^(^1^/^2^)} (1+r^2)^(^1^/^2^)rdrd\theta[/tex]

    Making the substitution u = 1 + r^2 gives:

    [tex] \frac{1}{3}\right) \int _{0}^{2Pi} 7d\theta = \frac{14}{3} Pi[/tex]

    The back of my book has 4/3*Pi. I don't understand how I am doing this problem wrong.
  2. jcsd
  3. Feb 25, 2010 #2


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    Your integrand should be zupper - zlower.
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