What is improper integrals?
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Improper integrals are a type of definite integral that involve either an infinite interval or an integrand that is not defined at one or more points within the interval of integration . They are often introduced in the second course of Calculus and can be difficult for students to grasp . The theory of definite integrals was originally developed for bounded functions defined on closed and bounded intervals . Improper integrals involving higher powers of arctanh, arctan, and arcsin have been examined using the recursive approach, leading to the establishment of explicit formulas in terms of π, ln2, the Riemann zeta function, and the Dirichlet beta function . An interesting method for evaluating certain integrals of the form $\int_0^\infty f(t)\,dt$ using Laplace transforms has also been discussed, providing a streamlined approach for computing the value of an integral .
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| Papers (5) | Insight |
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| The paper does not provide a direct definition or explanation of improper integrals. The paper focuses on examining specific classes of improper integrals involving inverse trigonometric and hyperbolic functions and establishing explicit formulas for their evaluation. | |
| The paper does not provide a direct definition of improper integrals. | |
| The paper does not provide information about improper integrals. | |
| Improper integrals are definite integrals with either an infinite interval or an integrand that is not defined at one or more points within the interval of integration. | |
| The paper does not provide a direct definition or explanation of improper integrals. The paper discusses an alternative criterion for an improper integral to diverge. |
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