Fundamental Theorem of Calculus - Intro and Proof of Part 2 of the Theorem

in MES Science4 months ago (edited)

In this video I introduce the second part of the fundamental theorem of calculus and also provide a simple proof for it. This theorem states that the integral from a to b of a function, f, is just equal to the antiderivative, F, at point b minus F at a. This greatly simplifies solving the integral which was defined in a very complex method using infinite rectangles. This is one of the most important theorems in all of mathematics so make sure you fully understand this!


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Fundamental Theorem of Calculus - Intro and Proof of Part 2 of the Theorem

Fundamental theorem of Calculus Part 2 Proof.jpg

Recap on FTC 1 and FTC 2

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Proof FTC 2

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Notes

Some Notes:

  • If we know the antiderivative F of f we can easily evaluate the integral by subtracting the values of F at the endpoints
  • Surprising that since the integral was defined by a sum of infinite rectangles from a to b, the solution using antiderivatives is very simple.

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This is very educative.