4.1 Modeling Accumulations
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.
ExamplesApproximate the area of an ellipse using 7 circumscribed rectangles in the first quadrant.
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.
AppletsApproximating Areas: Inscribed Polygons
VideosSee short videos of worked problems for this section.
ExercisesSee Exercises for 4.1 Modeling Accumulations (PDF).
Work online to solve the exercises for this section, or for any other section of the textbook.
Resources on the WebInformation on Newton
Biographical data from St. Andrew's University's Web site
Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
History of Calculus
Approximation of Areas
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel