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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

Select the first clip below to begin.

» Clip 1: Example of Estimation (8 min)
» Accompanying Notes (PDF)

From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006

» Clip 2: Example: Change of Variables (5 min)
» Accompanying Notes (PDF)

From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006

Download the complete lectures from this course:

» iTunes U
» Internet Archive

Recitation Video

 

Definite Integral by Substitution

Worked Example

 

Integration by Change of Variables

Lecture Video and Notes

Video Excerpts

Select the first clip below to begin.

» Clip 1: Substitution When u' Changes
  Sign (3 min)
» Accompanying Notes (PDF)

From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006

Download the complete lectures from this course:

» iTunes U
» Internet Archive

 

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