Question

What is the arclength of `f(x)=sqrt((x-1)(2x+2))-2x` on `x in [6,7]`?

Answer 1

`1.15037`

Explanation:

We have
`f(x)=sqrt((x-1)*2*(x+1))-2x`
`f(x)=sqrt(2)*sqrt(x^2-1)-2x`
So we get the integral

`int_6^7sqrt(1+(sqrt(2)*x/sqrt(x^2-1)-2)^2)dx`
With a numerical method we find
`approx 1.1.5037`