Question

What is the arc length of `f(t)=(1/sqrt(t+t^2),2-8t)` over `t in [1,3]`?

Answer 1

`approx 16.0071`

Explanation:

We hat
`x(t)=(t^2+t)^(-1/2)`
`x'(t)=-1/2*(2*t+1)/(t^2+t)^(3/2)`
`y(t)=2-8t`
`y'(t)=-8`
So we have to solve
`int_1^3sqrt(64+(-1/2*(2*t+1)/(t^2+t)^(3/2))^2)dt`
I have got only a numerical value.