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Explore the concept of improper integrals in this comprehensive lecture from Professor Leonard's Calculus 2 series. Delve into the intricacies of evaluating integrals with infinite limits or discontinuities within the interval of integration. Learn techniques for determining convergence or divergence of improper integrals and gain a deeper understanding of their applications in advanced calculus. Through clear explanations and numerous examples, master the skills necessary to tackle complex integration problems involving unbounded intervals or functions with vertical asymptotes.