Session 49: Applications of the Fundamental Theorem of Calculus

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Overview

In this session we see how definite integrals can be used in estimation, to find upper or lower bounds on an answer. Then we examine how the limits on the definite integral interact with substitutions.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Example of Estimation (00:08:00)

» Accompanying Notes (PDF)

From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: Example: Change of Variables (00:05:00)

» Accompanying Notes (PDF)

From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006

Recitation Video

 

Definite Integral by Substitution

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Worked Example

 

Integration by Change of Variables

Lecture Video and Notes

Video Excerpts

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» Clip 1: Substitution When u' Changes Sign (00:03:00)

» Accompanying Notes (PDF)

From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006

 

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