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Homework Help: Surface integral help.

  1. Feb 22, 2010 #1
    1. The problem statement, all variables and given/known data
    What is the area of the portion of the sphere [tex]x^{2}+y^{2}+(z-a)^{2}=a^{2}[/tex] that is inside the paraboloid [tex]z=x^{2}+y^{2}[/tex]

    2. Relevant equations
    [tex]\int\int_{S} dS[/tex]

    3. The attempt at a solution

    I used this

    [tex]\int\int_{S} dS=\int\int_{R}\sqrt{f^{2}_{x}+f^{2}_{y}+1}dx dy[/tex]

    And got

    [tex]=\int\int_{R}\frac{a}{\sqrt{a^{2}-x^{2}-y^{2}}}dx dy[/tex]

    I know that R is the projection of the surface on the xy plane, but I tried a few different ways to compute the boundaries but it never made sense. Maybe I'm just approaching it the wrong way. Anyone can help me with this?
  2. jcsd
  3. Feb 22, 2010 #2

    Gib Z

    User Avatar
    Homework Helper

    Can you please show us what you tried? Did you try solving for the bounds algebraically? Draw a diagram to aid you, and solve the equations simultaneously.
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