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dear in 2D this represents a circle and for circle this is relation b/w polar and Cartesian coordinate syste

See here you have to integrate F.dr around the closed circular path x2+y2=a2. so here are two variable in the integration x and y. But if we use parametric equation of a circle i.e...

because surface would be simply area. and area is in 2D so we consider it as above

hope u got it dear