find the length of the curve r(t)=2t^(3/2)i + cos(2t)j + sin(2t)k 0<t<1.
$\displaystyle x = 2t^{3 \over 2} $
$\displaystyle y = \cos (2t) $
$\displaystyle z = \sin (2t) $
then the length of the curve is
$\displaystyle \int_{0}^{1} \sqrt{ \big(\frac{dx}{dt}\big)^2 + \big(\frac {dy}{dt}\big)^2 + \big(\frac{dz}{dt}\big)^2} \ dt $