# What is the arclength of f(x)=1/sqrt((x+1)(2x-2)) on x in [3,4]?

Jun 3, 2018

$\approx 1.00235$

#### Explanation:

Wrting $f \left(x\right)$ in the following form

$f \left(x\right) = {\left(2 \left(x + 1\right) \left(x - 1\right)\right)}^{- \frac{1}{2}}$
so
$f ' \left(x\right) = - 2 \frac{x}{\sqrt{2 \left({x}^{2} - 1\right)}} ^ 3$
and we have
int_3^4sqrt(1+(-2x/sqrt(2(x^2-1))^3)dx
With a numerical method we get

$\approx 1.00235$