Determine whether the integral is convergent or divergent.

To determine the convergence of an integral, one typically examines the behavior of the integrand near points of discontinuity and at the limits of integration. For instance, if you are considering the integral of a function like 1/x from 1 to infinity, you'd evaluate its improper nature by assessing the limit as the upper bound approaches infinity. If the integral yields a finite result, it's convergent; if it diverges to infinity, it's divergent. Another common case involves using comparison tests. If you can find a smaller function that converges and is comparable to your integrand, you can establish convergence. Conversely, if there's a larger function that diverges, your integral might just follow suit. This technique helps to simplify your analysis and reach a conclusion more easily.