Overview
We can use antiderivatives to find the area bounded by some vertical line x=a, the graph of a function, the line x=b, and the x-axis. We can prove that this works by dividing that area up into infinitesimally thin rectangles.
Lecture Video and Notes
Video Excerpts
» Clip 1: Introduction to Definite Integrals (00:04:00)
From Lecture 18 of 18.01 Single Variable Calculus, Fall 2006
Clip 1: Introduction to Definite Integrals
> Download from iTunes U (MP4 - 104MB)
> Download from Internet Archive (MP4 - 104MB)
» Clip 2: Definition of Definite Integrals (00:03:00)
From Lecture 18 of 18.01 Single Variable Calculus, Fall 2006
Clip 2: Definition of Definite Integrals
> Download from iTunes U (MP4 - 104MB)
> Download from Internet Archive (MP4 - 104MB)
Worked Example
Integration Intuition