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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 (4 min)
» Accompanying Notes (PDF)

From Lecture 20 of 18.01 Single Variable Calculus, Fall 2006

» Clip 2: Using the Second Fundamental Theorem of
  Calculus (6 min)
» Accompanying Notes (PDF)

From Lecture 20 of 18.01 Single Variable Calculus, Fall 2006

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Recitation Video

 

Applying the Second Fundamental Theorem

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» iTunes U (MP4 - 9MB)
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Second Fundamental Theorem and Chain Rule

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Second Fundamental Theorem and Quadratic Approximation

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