Question

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

Answer 1

`approx 1.07667`

Explanation:

We get by the Quotient rule

`f'(x)=(2x(x-1)-(1+x^2))/(x-1)^2`
`f'(x)=(x^2-2x-1)/(x-1)^2`
so our integral is given by

`int_2^3sqrt(1+((x^2-2x-1)/(x-1)^2)^2)dx`

A numerical result is given by `approx 1.07667`