Applications Of The Definite Integrals: (lesson 3 of 3)
Arc Length
Arc Length=a∫b1+[f′(x)]2dx
Example 1:
Find the arc length of the graph of
y=6x3+2x1 on
[21,2].
Solution:
f′(x)s=21(x2−x21)==a∫b1+[f′(x)]→dx=21∫21+[21(x2−x21)]2dx==21∫2[41(x4+2x+x41)]dx=21∫2[21(x2+x21)]2dx==21∫221(x2+x21)dx=[21(3x3−x1)]212==1633
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