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

Jun 23, 2018

$7.26345$

#### Explanation:

we have
$x \left(t\right) = t - t \sqrt{t - 1}$
then
$x ' \left(t\right) = 1 - \sqrt{t - 1} - \frac{t}{2 \sqrt{t - 1}}$

$y ' \left(t\right) = - 2$

so we have to solve

${\int}_{1}^{4} \sqrt{{\left(1 - \sqrt{t - 1} - \frac{t}{2 \sqrt{t - 1}}\right)}^{2} + 4} \mathrm{dt}$