On-screen applet instructions: The applet depicts the total area between two curves, as well as the net area. In each case an integral formula is given. In the case of total area, explain the role of the absolute value and how it is evaluated over the interval of integration.

Examples Find the area of the region bounded by y2 = 2x and x – y = 4. Sketch the region. Find the area between and Sketch the region. Consider the region between the circles x2 + y2 = a2 and x2 + y2 = b2 in the first quadrant. Divide this region into two pieces with the curve defined by in the first quadrant. Find the ratio of the two regions created and sketch them. Videos See short videos of worked problems for this section. Quiz Take a quiz. Exercises See Exercises for 4.7 Areas Between Curves (PDF). Work online to solve the exercises for this section, or for any other section of the textbook.

Resources on the Web Information 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" Information on Leibniz 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" Calculus Applications Project Intermath Areas Between Curves Mathlet Visual Calculus

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4.6 Trapezoid Rule

Table of Contents

4.8 Volumes of Solids of Revolution

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