Consider the intersection,R, between two circles : x2+y2=2 and (x-2)2+y2=2
a) Find a 2-Dimensional vector field F=(M(x,y),N(x,y)) such that ∂N/∂x - ∂M/∂y=1
The Attempt at a Solution
There are other parts to the main question but I don't think I will have a problem with them. I know how to calculate the curl of F but I'm unsure of how to go about it so that the vector field relates to the intersection as we use F in an integral later on. What I thought of doing was integrating the curl function with respect to x or y in turn and trying to find M and N. I cant quite see how to involve the equations of the circles in all of this, if someone could point me in the right direction?