Chapter 17.3, Problem 35E

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.

35. ${\displaystyle \underset{C}{\int }F\cdot dr;}$C: r(t) = ⟨2t − 1, t² + t⟩, for 1 ≤ t ≤ 2