Session 51: The Second Fundamental Theorem of Calculus

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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

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» Clip 1: Second Fundamental Theorem of Calculus (00:04:00)

» Accompanying Notes (PDF)

From Lecture 20 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: Using the Second Fundamental Theorem of Calculus (00:06:00)

» Accompanying Notes (PDF)

From Lecture 20 of 18.01 Single Variable Calculus, Fall 2006

Recitation Video

 

Applying the Second Fundamental Theorem

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Second Fundamental Theorem and Chain Rule

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Second Fundamental Theorem and Quadratic Approximation

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