4.1 Modeling Accumulations



The issues to be studied in Chapter 4, Modeling Accumulations, are introduced. In particular, the problem of finding the area under a curve and above an interval on the x-axis is described. The method of accumulations is also illustrated; several examples are given. An agenda is established for the rest of the chapter.

By the end of your studying, you should know:

On-screen applet instructions: Use the pull-down menu to choose the number of subintervals and hence rectangles. A mouse click on the figure will toggle between a close view and a wider view of the circle.


Approximate the area of an ellipse using 7 circumscribed rectangles in the first quadrant.

Approximate the area of the quarter circle of radius 3 centered at the origin using n circumscribed rectangles, giving your answer in terms of n.

The graph of a stream's rate of flow over a 1-hour period is the graph of a sine curve. Assuming the rate of flow is measured every 10 minutes, starting at time 0, use the method of accumulation to aproximate the total volume of flow over this hour, accurate to 3 decimal places.


Approximating Areas: Inscribed Polygons

Approximating Area: Using Rectangles

Accumulation: River Flow

Accumulation: Distance Traveled


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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel