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Home Applications of the Integral Volumes of Solids of Revolution Examples Example 3
 
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Example 3

06_applications_of_the_integral-53.gif

Figure 6.2.11

The region R between the line y = 0 and the curve y = 2x - x2 is rotated about the y-axis to form a solid of revolution S. Find the volume of S. We use the cylindrical shell method because y is the dependent variable. We see that the curve crosses the x-axis at x = 0 and x = 2, and sketch the region in Figure 6.2.11. The volume is

V = 06_applications_of_the_integral-50.gif = 06_applications_of_the_integral-51.gif = 06_applications_of_the_integral-52.gif = (8/3)π
Home Applications of the Integral Volumes of Solids of Revolution Examples Example 3

Last Update: 2006-11-22