Question

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

Answer 1

`s=1.04487` if we compute from `x=(1+sqrt(3))` to `x=3`

there is no such length from `x=1` to `x=3`

Explanation:

observe the graph `f(x)=sqrt((x-1)(x+2)-3x)`
graph{sqrt((x-1)(x+2)-3x) [-5, 5, -2.5, 2.5]}

the possible length is from `x=(1+sqrt(3))` to `x=3` and not from `x=1` to `x=3`

`y'=(x-1)/sqrt(x^2-2x-2)`

`s=int_(1+sqrt(3))^3 sqrt(1+((x-1)/sqrt(x^2-2x-2))^2`