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Home Applications of the Integral Improper Integrals Examples Example 3
 
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Example 3

Find the length of the curve y = x2/3, 0 ≤ x ≤ 8. From Figure 6.7.3 the curve must have finite length. However, the derivative

06_applications_of_the_integral-405.gif

is undefined at x = 0. Thus the length formula gives an improper integral,

06_applications_of_the_integral-406.gif06_applications_of_the_integral-407.gif06_applications_of_the_integral-408.gif

06_applications_of_the_integral-409.gif06_applications_of_the_integral-410.gif

06_applications_of_the_integral-411.gif

Figure 6.7.3

Let it = 9x2/3 + 4, du = 6x-1/3 dx. The indefinite integral is

06_applications_of_the_integral-412.gif

Therefore06_applications_of_the_integral-413.gif
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Last Update: 2006-11-15