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

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Answer 1 · 2018-06-03T07:31:56

$approx 1.07667$

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 $approx 1.07667$

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