Question

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

Answer 1

`approx 1.00235`

Explanation:

Wrting `f(x)` in the following form

`f(x)=(2(x+1)(x-1))^(-1/2)`
so
`f'(x)=-2x/sqrt(2(x^2-1))^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`