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Session 52: Proving the Fundamental Theorem of Calculus

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Overview

Using the interpretation of the definite integral as describing the area under a graph, we prove the second fundamental theorem. Then we use FTC2 to prove FTC1.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Proof of the Second Fundamental Theorem of
  Calculus (3 min)
» Accompanying Notes (PDF)

From Lecture 20 of 18.01 Single Variable Calculus, Fall 2006

» Clip 2: Proof of the First Fundamental Theorem of
  Calculus (9 min)
» Accompanying Notes (PDF)

From Lecture 20 of 18.01 Single Variable Calculus, Fall 2006

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