Stoke's theorem application to curl theorem. I did. Please can you check it?

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Now, I need to apply stoke's theorem to curl theorem.

My teacher gave a hint.

Accourding to the hint, I accept $w=Pdy∧dz +Q dz∧dx + R dx∧dy$ $\in Ω^2(M)$

$dim(M)=2$

M is the subset of $\Bbb R^2$


Here is my solution.

$dw=\frac{\partial P}{\partial x}dx∧dy∧dz + \frac{\partial Q}{\partial y}dy∧dz∧dx +\frac{\partial R}{\partial z}dz∧dx∧dy$

Now I need to compute $\int_{Ω^2(M)}(P_x+Q_y+R_z)dx∧dy∧dz$

$=\int_{Ω^2(M)}(P_x+Q_y+R_z)dxdydz$


Are All things I did right? And is this enough to prove?

Thank you For all kind of helps:)