Question

For `f(t)= (t/(t+2)-t+1,t^2-t)` what is the distance between `f(2)` and `f(5)`?

Answer 1

18.2311

Explanation:

x-coordinate:
`x(t) = t/(t+2)-t+1`
`x'(t) = 2/(t+2)^2 - 1`

y-coordinate:
`y(t) = t^2 - t`
`y'(t) = 2t-1`

Limits of integration: `t=2 to t=5`

Total Distance = `int (sqrt((x'(t))^2 + (y'(t))^2)) dt` from `[2,5]`
`= int (sqrt((2/(t+2)^2 - 1)^2 + (2t-1)^2)) dt` from `[2,5]` = 18.2311