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Home Applications of the Integral Area of a Surface of Revolution Examples Example 5: Rotating a Curve About Xaxis and Yaxis  
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Example 5: Rotating a Curve About Xaxis and Yaxis
Let C be the curve y = x^{4}, 0 < x < 1. (see Figure 6.4.15) Figure 6.4.15 Set up an integral for the surface area generated by rotating the curve C about (a) the yaxis, (b) the xaxis (see Figure 6.4.16). (a) Figure 6.4.16 (a) dy/dx = 4x^{3} A = We cannot evaluate this integral, so we leave it in the above form. The Trapezoidal Rule can be used to get approximate values. When Δx = 1/10 the Trapezoidal Approximation is A ~ 6.42, error ≤ 0.26. (b)
Figure 6.4.16(b) A = The Trapezoidal Approximation when Δx = 1/10 is A ~ 3.582 error ≤ 0.9.


Home Applications of the Integral Area of a Surface of Revolution Examples Example 5: Rotating a Curve About Xaxis and Yaxis 