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Example 5: Rotating a Curve About X-axis and Y-axis

Let C be the curve

y = x4, 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 y-axis, (b) the x-axis (see Figure 6.4.16).



Figure 6.4.16 (a)

dy/dx = 4x3

A =06_applications_of_the_integral-231.gif


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.



Figure 6.4.16(b)      

A =06_applications_of_the_integral-233.gif


The Trapezoidal Approximation when Δx = 1/10 is A ~ 3.582 error ≤ 0.9.

Last Update: 2010-11-25