Chapter 17.3, Problem 37E

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 integral for the given curve C, if possible.

37. ${\displaystyle \underset{C}{\int }fdx+gdy;}$C is the path consisting of the line segment from A(6, 4) to B(1, 2) followed by the line segment from B(1, 2) to C(3, 6).