Chapter 6.2, Problem 98E

David and Sandra plan to evaluate line integral ${{\displaystyle \int }}_{c}F.dr,$ along a path in the xy-plane from (0, 0) to (1,1). The force field is $F\left(x,y\right)=\left(x+2y\right)i+\left(-x+y^2\right)j.$ David chooses the path that runs along the -axis from (0, 0) to (1, 0) and then runs along the vertical line x = 1 from (1, 0) to the final point (1, 1). Sandra chooses the direct path along the diagonal line y = x from (0, 0) to (1, 1). Whose line integral is larger and by how much?