Session 48: The Fundamental Theorem of Calculus

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Overview

Definite integrals "sum up" infinitesimal changes; one such change is adding the area of an infinitesimal rectangle. Another is traveling an infinitesimal distance forward. In this session we use definite integrals to compute distance traveled over time given a velocity function. We discuss negative integrands and then list a few properties of definite integrals.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Interpretation of the Fundamental Theorem (00:05:00)

» Accompanying Notes (PDF)

From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: The Fundamental Theorem and Negative Integrands (00:07:00)

» Accompanying Notes (PDF)

From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 3: Properties of Integrals (00:09:00)

» Accompanying Notes (PDF)

From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006

Worked Example

 

Integral of sin(x) + cos(x)

 

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