Methods of Integration of Functions in Several Variables

This lecture covers methods of integrating functions of several variables, including changing variables to polar coordinates and applying Fubini's theorem for changing the order of integration. The instructor explains the process step by step, emphasizing the importance of dividing the domain into regular areas. The lecture also delves into the concept of compact sets and continuous functions, particularly in the context of polar coordinates. Various examples are provided to illustrate the application of these methods, such as integrating functions over specific domains and understanding the additivity of integrals. The lecture concludes with a detailed explanation of the integrity of the integral and the significance of regular areas in the integration process.