Question

What is the arc length of `f(t)=(t-tsqrt(t-1),8-2t)` over `t in [1,4]`?

Answer 1

`7.26345`

Explanation:

we have
`x(t)=t-tsqrt(t-1)`
then
`x'(t)=1-sqrt(t-1)-t/(2sqrt(t-1))`

`y'(t)=-2`

so we have to solve

`int_1^4sqrt((1-sqrt(t-1)-t/(2sqrt(t-1)))^2+4)dt`