Green Theorem Proof

This lecture presents the proof of the Green theorem, which states that the integral of a vector field along the boundary of a domain is equal to the integral of the curve in the interior of the domain. The instructor demonstrates the proof using a general rectangle domain and a general vector field, explaining the computations step by step and emphasizing the importance of orientation. By parametrizing the boundary curves and computing the scalar products, the instructor shows that the two integrals are equal, concluding that the Green theorem holds for this generic case.