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Home Applications of the Integral Area of a Surface of Revolution Examples Example 3:
 
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Example 3:

The curve x = 2t2, y = t3, 0 ≤ t ≤ 1 is rotated about the y-axis. Find the area of the surface of revolution (Figure 6.4.11). We first find dx/dt and dy/dt and then apply the formula for area.

06_applications_of_the_integral-215.gif

06_applications_of_the_integral-216.gif

Figure 6.4.11

Let u = 16 + 9t2,

du = 18t dt, 06_applications_of_the_integral-217.gif, 06_applications_of_the_integral-218.gif.

Then

u = 16 at f = 0 and u = 25 at t = 1,

so

06_applications_of_the_integral-219.gif
Home Applications of the Integral Area of a Surface of Revolution Examples Example 3:

Last Update: 2006-11-22