How do I determine the convergence or divergence of an improper integral?

To determine the convergence or divergence of an improper integral, you must analyze the behavior of the integrand at the boundaries of the integration interval. This often involves comparing the improper integral to a known convergent or divergent integral using techniques such as the Comparison Test, the Limit Comparison Test, or the p-test for integrals. Additionally, you can apply specific criteria like the Direct Comparison Test or the Ratio Test to establish the integral’s behavior at infinity or near singularities.

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