Prove The Fundamental Theorem First!

This is a working draft of a piece.

Prove the Fundamental Theorem First! #

This semester, in my Calculus for Life Science class, I sketched a proof of the Fundamental Theorem of Calculus for students before introducing anti-derivatives. I found that this made the notion of anti-derivatives much more palatable. We proved the “net change” version of the FTC: $\displaystyle \int_a^b f^\prime(x) dx = f(b) - f(a)$. After doing a couple examples where we had $f^\prime(x)$ initially, we started doing examples where we had to massage a given $g(x)$ in to the form $f^\prime(x)$ for some explicit $f(x)$. This process is, of course, taking an anti-derivative. I found that this route avoided the sudden jump in complexity of taking anti-derivatives. It gave us a good reason to introduce the word “anti-derivative”.

Available here in the FYMSiC archive.

Published: Jun 24, 2025 @ 14:50.
Last Modified: Apr 29, 2026 @ 10:23.

Prove The Fundamental Theorem First!

Prove the Fundamental Theorem First! #

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