How do you find the arc length of the curve #y=1+6x^(3/2)# over the interval [0, 1]?

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Answer 1 · 2018-03-23T10:11:25

Use the arc length formula.

#y=1+6x^(3/2)#

#y'=9sqrtx#

Arc length is given by:

#L=int_0^1sqrt(1+81x)dx#

Integrate directly:

#L=2/243[(1+81x)^(3/2)]_0^1#

Hence

#L=2/243(82sqrt82-1)#