Integral Test
What is the purpose of an integral test?
The role of the integral test is to evaluate infinite series by examining an improper integral and deriving whether it converges or diverges.
What are the conditions needed for an integral test?
The conditions needed for the integral test are that the series must have positive, decreasing terms, and the corresponding function must be continuous for x ≥ 1.
Why do we need integral?
Integrals help find the total accumulation of something, like area or volume, by summing infinitely small pieces. They’re crucial in calculus for solving problems involving continuous change.
Does the integral test apply to alternating series?
Yes, the integral test can apply to alternating series as long as the terms of the series and the corresponding function meet the conditions of the integral test.
Why is it called an integral?
The term “integral” comes from the Latin word “integralis,” meaning “whole” or “complete.” It reflects the idea of finding the entire quantity or accumulation within a range.
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.