Show that the differential x y 0 0 is closed Show that it is

Last updated: 4/29/2023

Show that the differential x y 0 0 is closed Show that it is not independent of path on any annulus centered at 0 Solution r P OP 2 y y 2y dy x y udr ady x y x y Pdx Qdy x y2 x y Because OP Jy JQ Or the differential is closed and we can use Green s Theorem Q x y x y x 21 x y y Y f f ydx zdy dx dy 1 1 2 1 1 1 1 dx dy 2 r 2 0 72 z r Thus the line integral is not independent of path