Change of Variables: Integrability and Fubini's Theorem

This lecture covers the concept of changing variables in double integrals, focusing on the integrability of functions and the application of Fubini's theorem in R². The instructor explains how to handle integrals with different variable dependencies and symmetrical properties, emphasizing the importance of correctly identifying the domain of integration. Through examples and mathematical derivations, the lecture illustrates the process of transforming integrals and applying Fubini's theorem to simplify calculations. Special attention is given to the vertical and horizontal domains in R², showcasing the versatility of variable transformations in integral calculus.