How does one find the length of a curve parametrized by

$\displaystyle x = \sqrt{5}sin(2t)-2$ and $\displaystyle y=\sqrt{5}cos(2t)-\sqrt{3}$

from t = 0 to t = pi/4?

TIA

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- Aug 3rd 2009, 01:54 PMPTLFinding the length of a curve parametrized by...
How does one find the length of a curve parametrized by

$\displaystyle x = \sqrt{5}sin(2t)-2$ and $\displaystyle y=\sqrt{5}cos(2t)-\sqrt{3}$

from t = 0 to t = pi/4?

TIA - Aug 3rd 2009, 02:19 PMHaytham
$\displaystyle L=\int ds$

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

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