Let the differential 2-form = xdy dz + ydz dx + (1 - 2z)dx dy be defined in a star-like domain .
(a) Is closed?
(b) Is exact on D? If so, find a differential 1-form such that = d.
A) is neither closed nor exact
B) is both closed and exact, = ydx + 2xzdy - xydz
C) is closed but not exact
D) is exact but not closed, = ydx + 2xzdy + xydz
E) is both closed and exact, = -ydx - 2xzdy - xydz

Question

Let the differential 2-form   = xdy dz + ydz dx + (1 - 2z)dx dy be defined in a star-like domain  . 
(a) Is   closed?
(b) Is   exact on D? If so, find a differential 1-form   such that  = d.
A) is neither closed nor exact 
B) is both closed and exact, = ydx + 2xzdy - xydz 
C) is closed but not exact 
D) is exact but not closed, = ydx + 2xzdy + xydz 
E) is both closed and exact, = -ydx - 2xzdy - xydz

Quizplus · Accepted Answer

The Answer of Let the differential 2-form   = xdy dz + ydz dx + (1 - 2z)dx dy be defined in a star-like domain  . 
(a) Is   closed?
(b) Is   exact on D? If so, find a differential 1-form   such that  = d.
A) is neither closed nor exact 
B) is both closed and exact, = ydx + 2xzdy - xydz 
C) is closed but not exact 
D) is exact but not closed, = ydx + 2xzdy + xydz 
E) is both closed and exact, = -ydx - 2xzdy - xydz

Let the Differential 2-Form = Dz