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This lecture covers the concept of surface integrals over parameterized orientable surfaces, including the calculation of surface area and the use of normal vectors. It also discusses the application of surface integrals in various scenarios, such as determining flux and evaluating work. The instructor demonstrates how to compute surface integrals over different types of surfaces and emphasizes the importance of understanding the orientation of the surface. Examples and formulas are provided to illustrate the calculations and applications of surface integrals.