In this video I recap on my earlier videos on the two parts of the Fundamental Theorem and summarize the theorem as well as provide a brief history lesson on the importance of the theorem as it is one of the greatest inventions of the human mind!
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Fundamental Theorem of Calculus: Recap and Summary of the Theorem
Differentiation and Integration as Inverse Processes
Taking the two parts of the theorem together, it can be seen that differentiation and integration are inverse processes:
“Each undoes what the other does.”
Important Notes
- The Fundamental Theorem of Calculus is unquestionably the most important theorem in calculus and, indeed, ranks as one of the great accomplishments of the human mind.
- Before it was discovered, from the time of Eudoxus and Archimedes to the time of Galileo and Fermat, problems of finding areas, volumes, and lengths of curves were so difficult that only a genius could meet the challenge.
- But now, armed with the systematic method that Newton and Leibniz fashioned out of the Fundamental Theorem, we will see in the next videos to come that these challenging problems are accessible to all of us!