Chapter 15 - Topics In Vector Calculus - 15.2 Line Integrals - Exercises Set 15.2 - Page 1109: 17

True

Since \[ \mathbf{F} = f(x,y)\mathbf{i} + g(x,y)\mathbf{j} \] Then \[ \int \mathbf{F} \cdot d\mathbf{r} = \int_C (f(x,y)\mathbf{i} + g(x,y)\mathbf{j}) \cdot (d\mathbf{xi} + d\mathbf{yj}) = \int_C f(x,y)dx + g(x,y)dy \] Result: \[ True \]