```Date: Mar 20, 1998 8:44 PM
Author: Chris  & Sheila King
Subject: Integral as Accumulator...revisted

Back a month or so ago, we discussed on this list, the ability of ourstudents to recognize applications of the integral as accumulator.One proposed question dealt with whether our AB students would (fairly)be able to recognize that a set up for arc length actually measure acurve length. I've still not gotten to that particular application ofthe integral (I plan to some time before the AP exam, but after Easter).But, in the spirit of that discussion, I've been trying to do severaldifferent applications with my students. (We've not gotten to volume byslices yet...was supposed to do it this week just ended, but it gotdelayed...I hope to start it on Monday...am building a foam-board modelthis weekend for demonstration.) Well, we did several of the application problems in the Stewart book(the text I use) and also borrowed some out of the Larson text. I triedto stress to the students the importance of understanding why theintegral set up a certain way, and what it meant. I'm curious what one might think of my two test questions on this topic.Here they are:1. Consider a sphere which is expanding as time passes. The Area is afunction of time. A'(t) is the rate of change of the area with respectto time. Explain what the following integral represents:fnInt(A'(t), t, 3, 5)2. Considering the same sphere as in the previous problem, B(r) is thearea of the sphere as a function of the radius. Explain what thefollowing integral represents:fnInt(B(r), r, 3, 5)Any and all comments welcome.Sheila King------http://www.wenet.net/~cking/sheila/
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