10. (a) Consider the triangular region R in the plane with boundary curve C as shown below: 4. 2) C R Let F(r.y) - yi+ (a + 2)rj be a vector field in the plane. R'. Use Green's theorem in the plane to calculate F ar (b) Consider the region D in the plane. R', with boundary curve C as shown below D Suppose F(z, y) = M(r,y) it N(r. y) j is a vector field in the plane, R', which satisfies the condition that F = Vf for some smooth function / defined on R? Suppose also that F satisfies the conditions of Green's Theorem in the plane. Show that Al de + N dy - 0