What is the arclength of #f(t) = (t-sqrt(t-1),t^2/(t^2-1))# on #t in [2,3]#?
Result obtained using numerical integration, can't find closed form antiderivative:
First some definition and principles that will need to solve this:
Consider a vector function
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: