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Verify stoke's theorem

  1. Dec 6, 2009 #1
    Hello everybody,
    I am stuck on my homework. This question is giving me a headache, I've literally been staring at it for over 30 minutes. Perhaps someone here may be able to answer it (I hope), any help will be greatly appreciated:

    1. The problem statement, all variables and given/known data

    Legend:
    S= integral
    SS= double integral
    sub= boundary/limit a
    #^n= number raised to exponent n
    *= multiply

    -----------------------------------------------------------------------------------------------------------------
    Let S be the portion of the paraboloid: z = 9 - x^2 - y^2 which lies above the plane: z= 5, with normal vector N pointing upward (i.e. in the direction of increasing z), and let F be the vector field given by: F(x,y,z)= (x-yz)i + xzj. Verify Stoke's Theorem by evaluation each of the following:


    a) The line integral: S sub c (F dr), where C is the boundary of s, oriented counter-clockwise relative to N.


    b) The flux integral: SS sub s (curl F) * N dS



    2. Relevant equations

    Stoke's Theorem
    S sub c (F * dr) = S sub s S (curl F) * N ds



    3. The attempt at a solution

    I have no idea on how to start, im soo lost :(
     
  2. jcsd
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