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This lecture covers the topics of Taylor series and definite integrals. It starts by explaining the concept of Taylor series and its application in approximating functions. Then, it delves into the properties of definite integrals, including linearity and symmetry. The lecture also discusses the construction of definite integrals and the properties of integrals, such as linearity and the cancellation of positive and negative areas. Examples of indefinite integrals are provided, emphasizing the importance of finding primitives of functions.