Evaluate ∫F dot ds
F = < 1 - y/ (x^2 + y^2) , 1 + x/(x^2 + y^2) , e^z >
C is the curve z = x^2 + y^2 -4 and x + y + z = 100
The Attempt at a Solution
I don't think Stokes theorem applies since the vector field is undefined at the origin, so I'm trying a path integral according to ∫F(c(t) dot c'(t) dt for path c. The problem is that I combined the curve equations into a completed square that gave me a parameterization that I don't see how to integrate.
x^2 + y^2 - 4 = 100 - x - y
(x+1/2)^2 + (y+1/2) ^2 = 104.5
x = √104.5 cos t - 1/2
y = √104.5 sin t - 1/2
z = 100 - √104.5 cos t - √104.5 sin t
for t from 0 to 2∏
The resulting integral is an unholy mess. Am I missing something?
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