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Home Applications of the Integral Volumes of Solids of Revolution Examples Example 2
 
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Example 2

The region R between the curves y = 2 - x2 and y = x2 is rotated about the x-axis generating a solid S. Find the volume of S.

The curves y = 2 - x2 and y = x2 cross at x = +1. The region is sketched in Figure 6.2.8. The volume is

06_applications_of_the_integral-40.gif

06_applications_of_the_integral-41.gif

Figure 6.2.8

Warning:
When using the disc method for a region between two curves, the correct formula is

06_applications_of_the_integral-42.gif

or

06_applications_of_the_integral-43.gif

A common mistake is to subtract f(x) from g(x) before squaring.

Wrong:

06_applications_of_the_integral-44.gif

Wrong: (for Example 2):

06_applications_of_the_integral-45.gif
Home Applications of the Integral Volumes of Solids of Revolution Examples Example 2

Last Update: 2006-11-22