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How do I parameterize these surfaces?

  1. Dec 13, 2016 #1
    1. The problem statement, all variables and given/known data
    Parameterize ##S={ S }_{ 1 }\bigcup { { S }_{ 2 } } ##, where ##S_1## is the surface with equation ##x^2+y^2=4## bounded above by the graph of ##2y+z=6## and below by the ##xy## plane. ##S_2## is the bottom disk

    2. Relevant equations


    3. The attempt at a solution
    ##{ S }_{ 1 }=\left< 2cosu,2sinu,v \right> ,0\le u\le 2\pi ,0\le v\le 6-2y\\ { S }_{ 2 }=\left< rcosu,rsinu,0 \right> ,0\le u\le 2\pi ,0\le r\le 2##It doesn't make sense with the z boundaries because ##6-2y## isn't in terms of ##u## and ##v##...would it be ##6-4sinu##?
     
  2. jcsd
  3. Dec 14, 2016 #2

    BvU

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    I think that's the idea. I wouldn't know how to parametrize this in one single expression, ecxept also with a ##\cup## symbol (for the disc I would then use different parameter names).

    Note: The ##\ 0\le v \le 6-4\sin u \ ## isn't a parametrization yet (imho).

    ##\LaTeX## note: use \sin and \cos, etc. Much clearer
     
  4. Dec 14, 2016 #3
    this is OK in preparation for a surface integral right? Next I'd compose ##F## (the vector field) with ##S_1## and ##S_2## with two integrals, then dot that with the normal from each parameterization. But it's not clear which normal would I use? Inner or outer? is outer the conventional choice?
     
  5. Dec 14, 2016 #4

    BvU

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    What integral ? Have we seen the full problem statement yet ?
     
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