Overview
We can use definite integrals to create a new type of function -- one in which the variable is the upper limit of integration! The second fundamental theorem of calculus tells us, roughly, that the derivative of such a function equals the integrand.
Lecture Video and Notes
Video Excerpts
» Clip 1: Second Fundamental Theorem of Calculus (00:04:00)
From Lecture 20 of 18.01 Single Variable Calculus, Fall 2006
Clip 1: Second Fundamental Theorem of Calculus
> Download from iTunes U (MP4 - 109MB)
> Download from Internet Archive (MP4 - 109MB)
» Clip 2: Using the Second Fundamental Theorem of Calculus (00:06:00)
From Lecture 20 of 18.01 Single Variable Calculus, Fall 2006
Clip 2: Using the Second Fundamental Theorem of Calculus
> Download from iTunes U (MP4 - 109MB)
> Download from Internet Archive (MP4 - 109MB)
Recitation Video
Applying the Second Fundamental Theorem
> Download from iTunes U (MP4 - 9MB)
> Download from Internet Archive (MP4 - 9MB)
Second Fundamental Theorem and Chain Rule
> Download from iTunes U (MP4 - 11MB)
> Download from Internet Archive (MP4 - 11MB)
Second Fundamental Theorem and Quadratic Approximation
> Download from iTunes U (MP4 - 17MB)
> Download from Internet Archive (MP4 - 17MB)