How do I apply Stokes theorem on non contactable domain

39 Views Asked by At

Vector field is given by and I need to find line integral of G on the line defined as the intersection of $x+y+z=2$ and $x^2+y^2=z$.

I know how to do this in general case when vector field is continuously differentiable on the region that curve bounds. However this region is not contractile so I can’t apply Stokes theorem immediately.

Any idea what can be good approach in solving this kind of problems? enter image description here