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Integrating Power Series, Single Variable Calculus

In this lesson, we start integrating power series, focusing on term-by-term integration to create new power series representations for functions. We start with familiar functions and their power series, then progress to anti-differentiate both sides, illustrating the process with several examples. The radius of convergence R will be the same. We look at two examples of using this to handle difficult integrals. (Previous video:    • Differentiating Power Series, Single Varia...  ) Key Points Power Series Integration: A power series can be integrated term-by-term to form a new power series. Radius of Convergence: The radius of convergence for an integrated power series remains the same as the original. Practical Application: Power series integration is useful for functions where traditional antiderivative methods are not feasible. Antiderivative Representation: For a function with a known power series, its antiderivative can be represented by a new power series. Estimating Definite Integrals: Power series can be used to estimate definite integrals, especially with alternating series, where the Alternating Series Remainder theorem is applicable. Review Alternating Series here:    • Alternating Series Test (AST) for Infinite...   #mathematics #math #calculus #sequencesandseries #powerseries #iitjammathematics