Let $\omega=z d x \wedge d y,$ a 2-form in $\mathbb{R}^{3}$. Let $M = \{(x,y,z) \in \mathbb{R}^3 : z = 1 + x^2 + y^2\}$. Determine whether the restriction of $\omega$ to M is exact. If so, construct a 1-form $\eta$ on M such that $\omega = d\eta$.
This is an old exam question, and I am not sure how I should approach it. If it is a one form I would try finding a closed curve and integrate the form over it, but with a 2-form I cannot think of any efficient tools to solve this.