Since the field vectors and the curve that is the intersection of surfaces:
and
Find the circulation of F arrond the
My solution:
curl F = (1,1,1)
Surface S1:
Normal:
Surface S2:
Normal:
Circulation:
It is correct ?
No-- you kind of missed the point
alpha is the curve of intersection of the plane and the cylinder
See the attachment for the details where the line integral is computed directly
If you use Stokes theorem then your surface is z= 1-x-y over a circle of radius 1
N = i + j + k
curl F*N = 3 int(curlF*NdA) = 3*area = 3 pi which is what we obtain computing the line integral directly