18.01SC | Fall 2010 | Undergraduate

Single Variable Calculus

Part A: Definition of the Definite Integral and First Fundamental Theorem

Session 49: Applications of the Fundamental Theorem of Calculus

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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

Clip 1: Example of Estimation

Clip 2: Example: Change of Variables

Recitation Video

Definite Integral by Substitution

Worked Example

Integration by Change of Variables

Lecture Video and Notes

Video Excerpts

Clip 1: Substitution When u’ Changes Sign

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Course Info

As Taught In
Fall 2010
Learning Resource Types
Exams with Solutions
Lecture Notes
Lecture Videos
Problem Sets with Solutions
Recitation Videos