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Session 91: Improper Integrals

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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

Select the first clip below to begin.

» Clip 1: Introduction to Improper Integrals (4 min)
» Accompanying Notes (PDF)

From Lecture 36 of 18.01 Single Variable Calculus, Fall 2006

» Clip 2: Integral of e−kx (11 min)
» Accompanying Notes (PDF)

From Lecture 36 of 18.01 Single Variable Calculus, Fall 2006

» Clip 3: Integral of e−x2 (2 min)
» Accompanying Notes (PDF)

From Lecture 36 of 18.01 Single Variable Calculus, Fall 2006

» Clip 4: Integral of 1/x (3 min)
» Accompanying Notes (PDF)

From Lecture 36 of 18.01 Single Variable Calculus, Fall 2006

Download the complete lectures from this course:

» iTunes U
» Internet Archive

Worked Example

 

Integrating 1/(5x + 2)2 from 1 to Infinity

Recitation Video

 

A Solid With Finite Volume and Infinite Cross Section

Lecture Video and Notes

Video Excerpts

Select the first clip below to begin.

» Clip 1: Integral of 1/(xp) (6 min)
» Accompanying Notes (PDF)

From Lecture 36 of 18.01 Single Variable Calculus, Fall 2006

Download the complete lectures from this course:

» iTunes U
» Internet Archive

Recitation Video

 

Improper Integrals

 

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