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

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

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