Integral Calculus of Functions in Several Variables

This lecture covers the integration of functions in several variables, closed box, Darboux sums, integrability of a continuous function on a closed box, and properties of the integral. It also includes Fubini's theorem on a closed box. The lecture discusses the definition of a closed box as a subset of R^n, the volume of a closed box, the concept of Darboux sums, and the integrability of a function on a closed box. It explores the volume of a closed set under a surface, the Fubini theorem for a closed box, and the integration order. The lecture concludes with the properties of the integral, including additivity and integrability conditions.