Comments on: A Calculus Analogy: Integrals as Multiplication

By: kalid

kalid — Thu, 29 Dec 2011 02:52:02 +0000

@Anonymous: Yes, indefinite integrals are an interesting beast. In fact, there’s not really a “process” for them, it’s more “What function has the derivative that we want?” I.e., we aren’t finding integrals directly, we know them because such and such a function has the derivative we’re looking for. This confused me a for a long, long time as finding derivatives is so mechanical, and finding integrals so free-flowing.

By: Anonymous

Anonymous — Wed, 28 Dec 2011 23:25:42 +0000

Even though this approach “makes sense” when looking at definite integrals (which by definition are Riemann sums), the mental model of “multiplication” has almost nothing to do with the process of integrating (or, rather, indefinite integration) which is a purely algebraic (as opposed to arithmetic) process.

By: The Weinerworks » Physics! #16: University Physics 2.6

The Weinerworks » Physics! #16: University Physics 2.6 — Thu, 27 Oct 2011 17:52:58 +0000

[...] is finding the area under a curve.” This is technically true, but not terribly useful. As Kalid from BetterExplained notes, saying that be like saying multiplication is finding the area of a rectangle. It’s a [...]

By: Understanding Calculus With A Bank Account Metaphor | BetterExplained

Understanding Calculus With A Bank Account Metaphor | BetterExplained — Thu, 17 Mar 2011 17:35:19 +0000

[...] to see integration as a better multiplication 6 Comments Posted March 16, 2011, under Calculus,Math Tags: Related [...]