If c is the line segment connecting (x1,y1) to (x2,y2), show that the line integral of xdy-ydx=x1y2- is in a chapter about green's theorem don't answer if you really don't know or understand this kind of stuff.

Green's theorem doesn't really apply here. GT relates the line integral over some *closed* connected contour that bounds some region (like a circular path that serves as the boundary to a disk). A line segment doesn't form a region since it's completely one-dimensional.

At any rate, we can still compute the line integral just fine. It's just that GT is irrelevant.

We parameterize the line segment by




with . Then we find the differential:




with .

Here, the line integral is







as required.