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

##### 1 Answer

Result obtained using numerical integration, can't find closed form antiderivative:

#### Explanation:

First some definition and principles that will need to solve this:

Consider a vector function

with

Knowing this we are asked to find the length of the parametric curve given by

let's take the derivative of f(t):

Now square each term and take the square root and integrate:

This integral you have to integrate numerically, it does not have a close form antiderivative. You can us any online or fancy calculator"

My approximation is: