The Integral Test is a method used in calculus to determine the convergence or divergence of an infinite series. It applies to series of the form ∑a_n, where a_n is a positive, continuous, and decreasing function. If the improper integral ∫f(x) dx from a to ∞ converges, then the series ∑a_n also converges. Conversely, if the integral diverges, so does the series.
This test is particularly useful for series that can be expressed as functions of x. By comparing the series to the corresponding integral, mathematicians can easily assess the behavior of the series without needing to sum its terms directly.