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

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Answer 1 · 2018-05-16T06:37:55

Use the arc length formula.

$f (x) = 2 {(x - 1)}^{\frac{3}{2}}$ $f(x)=2(x−1)^(3/2)$

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

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:

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

How do you find the arc length of the curve f(x)=2(x-1)^(3/2)f(x)=2(x−1)32f(x)=2(x-1)^(3/2) over the interval [1,5]?