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
» Clip 1: Interpretation of the Fundamental Theorem (00:05:00)
From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006
Clip 1: Interpretation of the Fundamental Theorem
> Download from iTunes U (MP4 - 106MB)
> Download from Internet Archive (MP4 - 106MB)
» Clip 2: The Fundamental Theorem and Negative Integrands (00:07:00)
From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006
Clip 2: The Fundamental Theorem and Negative Integrands
> Download from iTunes U (MP4 - 106MB)
> Download from Internet Archive (MP4 - 106MB)
» Clip 3: Properties of Integrals (00:09:00)
From Lecture 19 of 18.01 Single Variable Calculus, Fall 2006
Worked Example
Integral of sin(x) + cos(x)