Question

What is the arc length of `f(x)=ln(x)/x` on `x in [3,5]`?

Answer 1

You'll need some approximation techniques to get an answer.

Explanation:

`f'(x) = (1-lnx)/x^2`

So the arc length is given by:

`int_3^5 sqrt(1+(1-lnx)^2/x^4) dx`

The length is a bit more than `2`. (According to Wolfram Alpha)