So say for a line integral, the curve C is given by y = sqrt(x), from point (1,1) to (4,2); In my integral I have some integrand* dy. Say I wanted to change the dy to dx. From whats given : y = sqrt(x); dy = 1/(2sqrt(x) ) dx; I could just substitute that instead for dy. But whats the difference if I do this : y = sqrt(x) y^2 = x 2y dy = dx dy = dx/2y So how is the former different from the latter. I mean I see that y is integrated for the second one, but what does it represent? Can you explain me the difference between the two, does not have to be geometrically, but will be appreciated.