Comments on: Reddit discussion considered productive

By: Kisakookoo

Kisakookoo — Wed, 24 Jan 2007 05:16:30 +0000

Hi! Why I can’t fill my info in profile? Can somebody help me?
My login is Kisakookoo!

By: dr. k

dr. k — Fri, 19 Jan 2007 03:54:46 +0000

I mean, let’s say you have f(x) = x^3

Integral from (-a) to a of x^3 is 0. But the *area* is 2*integral of 0 to a of x^3.

See?

By: Ben Franksen

Ben Franksen — Sat, 23 Dec 2006 22:59:58 +0000

You write: “Moreover, this pair of analogies [derivative-as-angle, integral-as-area] doesn’t yield the basic result of the field (the fundamental theorem of calculus), and working directly with them forever means losing out big time…”

Derivative-as-angle is a bad idea to start with. It doesn’t even generalize properly to a two-dimensional domain. It should have long ago been completely replaced by the much more general (and still easy to understand) local-approximation-by-a-linear-function.

However, integral-as-area generalizes quite well, even to the most abstract setting (measurable function on a measure space). What doesn’t generalize is one concrete and very simple-minded method of /calculating/ the integral (the so-called ‘Riemann-Integral’).

By: Julian Morrison

Julian Morrison — Thu, 14 Dec 2006 16:40:06 +0000

“interact” is your friend.