Improper Integrals
In this lesson on improper integrals, we learn how to interpret and evaluate integrals over unbounded and bounded intervals. We define convergence and divergence for these types of integrals, and explore specific examples of each. We also discuss the fundamental theorem of calculus and notation in the context of improper integrals over unbounded intervals. With clear explanations and visual aids, this lesson provides a comprehensive understanding of improper integrals.
Integrals over unbounded intervals. Integrals over bounded intervals of functions that are unbounded near an endpoint. Comparison test for convergence/divergence.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
- How do you find improper integrals over unbounded intervals?
- When does an improper integral converge or diverge?
- What is an improper integral?
- What is the integral of 1/x^3 from 1 to infinity?
- What is the integral of 1/square root of x from 1 to infinity?
- What is the integral of 1/x^p from 1 to infinity?
- When does the integral of 1/x^p converge or diverge?
- How do you find the improper integral of unbounded functions over bounded intervals?
- What is the integral of tan x between 0 and pi/2?
- What is the comparison test for convergence?
- How do you use the comparison test to check if an integral converges or diverges?
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Staff Review
This video begins to introduce convergence and divergence of improper integrals using limits. There are several examples shown, including some very useful and strategic examples that will be used in later videos. The comparison test for convergence is also introduced. This is a very important video for understanding the remainder of Calculus.
