4.1 Modeling Accumulations

By the end of your studying, you should know:
Onscreen applet instructions:
Use the pulldown 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.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 1hour 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 PolygonsApproximating Area: Using Rectangles Accumulation: Distance Traveled VideosSee short videos of worked problems for this section.
QuizExercisesSee 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 NewtonBiographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Information on Leibniz
Calculus Applications
History of Calculus
Approximation of Areas

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3.7 Case Study: Population Modeling  Table of Contents  4.2 The Definite Integral 
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel