# Math Help - arc length

1. ## arc length

how to compute the arclength function $s(t)$with the curve $r=(e^t cos(-3t),e^t sin(-3t),e^t)$....i got stuck when i was doing the derivative parts.

And also how to find the length of curve if i given two points with $r(t)$, for example, if i have $r(t)=(10t,5t^2,5 Int)$ and i have to find the length of curve with points, $(10,5,0)$ and $(50,125, 5 In(5))
$

Help =( Plz help..

2. for the second part you should notice the points given are when t=1 and t=5 therefore it would be

$s=\int_{1}^{5}\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{d t})^2+(\frac{dz}{dt})^2}dt$

NB with latex you write the natural log as \ln to get $\ln$