(a) Show that the following differential is exact: dz = (ye xy )dx + (xe ey )dy....

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(a) Show that the following differential is exact:

dz = (yexy)dx + (xeey)dy.

(b) Calculate the line integral ʃc dz on the line segment from (0,0) to (2,2). On this line segment, y = x and x = y.
(c) Calculate the line integral ʃc dz on the path going from (0,0) to (0,2) and then to (2,2) (a rectangular path).

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