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Simplify the radical by breaking the radicand up into a product of known factors.
3
11- \frac{1}{2} y=3+6x
Taking y to the other side;
11-3-6x= \frac{1}{2} y
8-6x= \frac{1}{2}y
Multiply each side by 2
16-12x=y
y=16-12x
Stokes' theorem equates the line integral of 
along the curve to the surface integral of the curl of over any surface with the given curve as its boundary. The simplest such surface is the triangle with vertices (1,0,1), (0,1,0), and (0,0,1).
Parameterize this triangle (call it 
) by
with 
and 
. Take the normal vector to to be
Divide this vector by its norm to get the unit normal vector. Note that this assumes a "positive" orientation, so that the boundary of is traversed in the counterclockwise direction when viewed from above.
Compute the curl of :
Then by Stokes' theorem,
where
The integral thus reduces to
