Use the fundamental theorem of line integrals to calculate r c ~f â·d~r exactly, if ~f = 2x 1/3~i+e y/7 ~j, and c is the quarter of the unit circle in the first quadrant, traced counterclockwise from (1,0) to (0,1).

Assuming the vector field is , we want to find a scalar function such that . We require




Integrating both sides of the first PDE with respect to gives



Differentiating with respect to gives






Such a scalar function exists, so the fundamental theorem holds and any integral along any path is determined exactly by its endpoints. In this case,

Iwould say false, not positive but if prices went up for both stores, technically there will be less buyers?