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Surface Integral

  1. May 5, 2013 #1
    1. The problem statement, all variables and given/known data

    Evaluate ∫∫σ3x2 + 3y2 + 3z2 dS
    where σ is the part of the cylinder x2 + y2 = 4 between the planes z = 0
    , and z = 1, together with the top, and bottom disks.

    2. Relevant equations
    Surface integrals, maybe divergence theorem?


    3. The attempt at a solution
    I am having trouble knowing where to start with this one. I think I need to do a surface integral, but maybe with more than one surface? If that is right then what would I do for the cylinder side? How would I handle the z in the integral?
     
  2. jcsd
  3. May 5, 2013 #2

    SteamKing

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    What is the value of z at the top and bottom of the cylinder?

    What is the equation of the surface in between the top and bottom disks? Hint: it's a constant
     
  4. May 5, 2013 #3

    haruspex

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    I would start the integration over the curved surface by converting to cylindrical coordinates.
     
  5. May 6, 2013 #4
    Ok so I see that z = 0, and z = 1. What about the sides? Do I have to do them in three separate integrals?
     
  6. May 6, 2013 #5

    haruspex

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    Yes.
     
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