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Example 2: Curve

06_applications_of_the_integral-203.gif

Figure 6.4.8

The curve

y = ½x2, 0 ≤ x ≤ 1,

is rotated about the y-axis (Figure 6.4.8). Find the area of the surface of revolution.

06_applications_of_the_integral-197.gif = x,

A =06_applications_of_the_integral-198.gif

=06_applications_of_the_integral-200.gif

=06_applications_of_the_integral-202.gif (where u = 1 + x2)

= 06_applications_of_the_integral-199.gif

=06_applications_of_the_integral-201.gif

 


Last Update: 2006-11-22