Improper Integrals

Ravinder Kumar

The concept of improper integral is introduced. Examples demonstrate how to find convergence/divergence of the two types of improper integrals. A comparison test for improper integrals is used in some examples. To make full use of GeoGebra applets please install latest version of GeoGebra from

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About the publisher

The author has taught mathematics for fifty years at several colleges and universities, including Delhi University (India), Alcorn State University, Tougaloo College (USA), and one summer teaching assignment at Brown University (2013). The author has used several different technologies in his teaching to help students learn mathematical concepts in various courses. In this course, divided into several topics, the author is presenting Calculus I & II for flipped classroom. Research Interests include Commutative Algebra and Instructional Technologies. The author thanks all his students and colleagues over the years with whom he has had academic interactions. Special thanks to my wife, Kanchan Manaktala, former professor of mathematics at Gargi College, Delhi University, India, and Alcorn State University, for her continued support.


Improper Integrals

About this course

Flipped classroom strategy consists of students self-studying the content of a topic provided by instructor. The instructor uses class hours to discuss questions, enhance student understanding, and help solve problems from the book. Spending a class hour to introduce students to the concepts in the flipped class lesson is found to be helpful. This 28th topic in Flipped Classroom Lessons in Calculus discusses improper integrals. We have used interactive Desmos graphs, Geogebra applets, and videos to help students learn on their own. Concept-check quiz serves as a self-check of concepts.