Overview
Integration allows us to find the area under the curve. Improper integrals let us find this area (if it's well defined) even when that curve extends to infinity. Knowing whether the area under a graph up to a large, finite value of x is significantly different from the area under the entire graph can help us simplify calculations and avoid approximation errors.
Lecture Video and Notes
Video Excerpts
» Clip 1: Introduction to Improper Integrals (00:04:00)
From Lecture 36 of 18.01 Single Variable Calculus, Fall 2006
Clip 1: Introduction to Improper Integrals
> Download from iTunes U (MP4 - 109MB)
> Download from Internet Archive (MP4 - 109MB)
Worked Example
Integrating 1/(5x + 2)2 from 1 to Infinity
Recitation Video
A Solid With Finite Volume and Infinite Cross Section
> Download from iTunes U (MP4 - 13MB)
> Download from Internet Archive (MP4 - 13MB)
Lecture Video and Notes
Video Excerpts
» Clip 1: Integral of 1/(xp) (00:06:00)
From Lecture 36 of 18.01 Single Variable Calculus, Fall 2006
Recitation Video
Improper Integrals
> Download from iTunes U (MP4 - 43MB)
> Download from Internet Archive (MP4 - 43MB)