Multiple Integrals: Defining Integrals of Functions in R^2

This lecture covers the definition of double integrals for functions of two variables over a domain in the plane R^2. It explains how to represent the integral of a positive, continuous function as the volume of a solid bounded by the function's graph, the Oxy plane, and vertical lines. The lecture also discusses approximating the volume using partitions and choosing points within each piece of the domain.