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




Re: Riemann Definition
Posted:
Dec 15, 1993 8:42 PM


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 24hour day. When I wondered aloud what the evening weather reporters mean when they talk about the "average" temperature ... The students became intrigued by 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 ab. 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)



