Question

What is the arclength of `f(t) = (t^3-t^2+5t,9t)` on `t in [1,4]`?

Answer 1

Use `L = int_1^4 (sqrt(((d(x(t)))/dt)^2 + ((dy(t))/dt)^2))dt` where `x(t) = t^3 - t^2 + 5t` and `y(t) = 9t`

Explanation:

`L = int_1^4 (sqrt((3t^2 - 2t + 5)^2 + 9^2))dt`

`L ~~ 70.05`