# Finding the length of a curve parametrized by...

• Aug 3rd 2009, 01:54 PM
PTL
Finding the length of a curve parametrized by...
How does one find the length of a curve parametrized by
$x = \sqrt{5}sin(2t)-2$ and $y=\sqrt{5}cos(2t)-\sqrt{3}$
from t = 0 to t = pi/4?

TIA
• Aug 3rd 2009, 02:19 PM
Haytham
$L=\int ds$

$L=\int \sqrt{dx^2+dy^2}$

$L=\int_0^{\frac{\pi}{4}} \sqrt{\left( \frac {dx}{dt} \right)^2+\left( \frac {dy}{dt} \right)^2} dt$