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:

Legend:

S= integral

SS= double integral

sub= boundary/limit a

#^n= number raised to exponent n

*= multiply

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Let S be the portion of the paraboloid:z = 9 - x^2 - y^2which 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