Can a differential form on all of R² be closed but not exact?

[Niles]

Homework Statement

Hi all

I can find a differential form defined on R²\{0,0}, which is closed but not exact, but is it possible to find a differential form defined on all R², which is closed but not exact?

 

[HallsofIvy]

No, it isn't. That is, essentially, Stoke's theorem.