How do you find the arc length of the curve #f(x)=2(x-1)^(3/2)# over the interval [1,5]?

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Answer 1 · 2018-05-16T06:37:55

Use the arc length formula.

#f(x)=2(x−1)^(3/2)#

#f'(x)=3sqrt(x-1)#

Arc length is given by:

#L=int_1^5sqrt(1+9(x-1))dx#

Simplify:

#L=int_1^5sqrt(9x-8)dx#

Integrate directly:

#L=2/27[(9x-8)^(3/2)]_1^5#

Hence:

#L=2/27(37^(3/2)-1)#