Chapter 17.3, Problem 36E

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.

36. ${\displaystyle \underset{C}{\overset{}{\int }}F·Tds;}$C is a smooth curve from (1, 2) to (6, 4).