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Topic: Re: Riemann Definition
Replies: 1   Last Post: Dec 16, 1993 12:22 AM

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NAME \ Barbara Reynolds, aka BER\

Posts: 30
Registered: 12/8/04
Re: Riemann Definition
Posted: Dec 15, 1993 8:42 PM
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In reply to Mark Janeba's question about how to convince students that
the formula for the average of f(x) on the interval [a,b] is reasonable:

Actually, recently my Calc 2 students "convinced" me that the formula
is reasonable. We were discussing a function that supposedly gave the
temperature as a function of time over the course of a 24-hour day.
When I wondered aloud what the evening weather reporters mean when they
talk about the "average" temperature ... The students became intrigued
this and a lively discussion followed. They reasoned that to average
something, we generally add everything up and divide by the total somehow.
So they constructed a Riemann sum ... so much for "adding it all up".
They argued for a while about what to divide by, and came to a consensus
that it would be reasonable to divide by the length of the interval, or
by |a-b|. The entire discussion took only about 30 minutes. It was
one of those moments when I had the grace to stand out of the way and
let the students develop the idea themselves.

BER (aka Barbara Reynolds, Cardinal Stritch College, Milwaukee, WI)

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