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Gauss's Theorem

  1. Nov 24, 2009 #1
    1. The problem statement, all variables and given/known data

    C is triangle (0,0), (4,0), (0,3). R is the enclosed region. Compute the following integral, where n is the outward pointing normal:

    [tex] \int_{C} \left(4x-y^{2}\right)n^{1}ds [/tex]

    where [tex] n^{1} = \widehat{i} \cdot \widehat{n} [/tex]

    2. Relevant equations



    3. The attempt at a solution

    I can't remember how to get the normal vector, can someone start me out there?
     
  2. jcsd
  3. Nov 24, 2009 #2

    Dick

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    There are three normal vectors, one for each side of the triangle that encloses the region. If the vector (a,b) is a tangent to a side then (-b,a) is a normal, isn't it? It's not necessarily a unit normal, but you should know how to fix that. Is that enough to get you started?
     
  4. Nov 26, 2009 #3
    So to evaluate this integral, should I separate it into 3 sub integrals over the 3 sides, using the corresponding normals?
     
  5. Nov 26, 2009 #4
    Also, is it necessary to parameterize before integrating? I'm getting hung up on the little details and missing then big picture.
     
  6. Nov 27, 2009 #5

    Dick

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    Yes, separate it into three integrals. Decide which direction around the triangle you are going. Then parameterize each side by length, integrate and add them up.
     
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