Question

What is the arclength of `f(t) = (e^(t)-e^(t^2)/t,t^2-1)` on `t in [1,3]`?

Answer 1

`approx 2681.58`

Explanation:

With
`x(t)=e^t-e^(t^2)/t` we get

`x'(t)=e^t-2e^(t^2)+e^(t^2)/t^2`

`y(t)=t^2-1`
so

`y'(t)=2t`
and we have to solve

`int_1^3sqrt((e^t-2e^(t^2)+e^(t^2)/t)^2+(2t)^2)dt approx 2681.58`