Applications of Integral Test
The applications of integral tests are as follows:
- Determining convergence of series with non-elementary terms.
- Analyzing the convergence of alternating series.
- Estimating the sum of series with known integrals.
- Investigating the convergence of power series.
- Studying the behavior of series involving trigonometric functions.
Integral Test
Integral Test is one of the simplest methods in calculus taught in terms of proving convergence or divergence in a given infinite series. It exhibits a connection between a series and an improper integral. By comparing a series to the integral of its terms, one can draw certain conclusions about the series. This test is particularly useful when dealing with series that involve functions that are difficult to analyze directly.
In this article, we will learn in detail about integral test, condition for integral test, its application and solved examples based on it.