Chapter 17.3, Problem 38E

Applying the Fundamental Theorem of Line integrals Suppose the vector field F is continuous on ℝ², F = ⟨f, g⟩ = ∇φ,

φ(1, 2) = 7, φ(3, 6) = 10

and φ(6, 4) = 20. Evaluate the following integrals for the given curve C, if possible.

38. ${\displaystyle \underset{C}{\oint }F\cdot dr;}$C is a circle, oriented clockwise, starting and ending at the point A(6, 4)