General Stokes' Theorem

Theorem
If $$\omega$$ is any smooth $$(n-1) \ $$-form on a smooth $$n \ $$-dimensional manifold $$X^n \ $$, then


 * $$\int_{\partial X} \omega = \int_X d \omega$$

where $$d\omega \ $$ is the exterior derivative of $$\omega \ $$.