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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 = 2t^{2}, y = t^{3}, 0 ≤ t ≤ 1 is rotated about the yaxis. 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. Figure 6.4.11 Let u = 16 + 9t^{2}, du = 18t dt, , . Then u = 16 at f = 0 and u = 25 at t = 1, so


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