Question

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

Answer 1

`1.01941`

Explanation:

Differentiaitng
`f(x)=arctan(2x)/x` with respect to `x`
we get

`f'(x)=2/(x(1+4x^2))-arctan(2x)/x^2`
so we have to solve the integral
`int_2^3sqrt(1+(2/(x*(1+4x^2))-arctan(2x)/x^2)^2)dxapprox 1.01941`