Verify stoke's theorem

  • #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:

Homework Statement



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



Homework Equations



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



The Attempt at a Solution



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

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