Integral Calculus: Techniques and Applications

This lecture covers the techniques and applications of integral calculus, including the concept of partitioning intervals, calculating areas under graphs, Darboux sums, and the fundamental theorem of calculus. It also explores the properties of continuous functions and the interpretation of integrals as areas. The instructor demonstrates how to compute areas under curves using regular subdivisions and the division of intervals into equal parts. Various methods for approximating integrals are discussed, such as Riemann sums and Darboux sums. The lecture concludes with the definition of the integral of a function and its relationship to the limit of Riemann sums.