Answer
$10.3311$
Work Step by Step
Given: $r(t)=\lt \cos \pi t, 2t,\sin 2 \pi t$; $0 \leq t \leq 2$
To calculate the length of the curve we will have to use the formula:
$L=\int_a^b |r'(t)| dt$
Thus,
$r'(t)=\lt -\pi \sin \pi t, 2,2 \pi \cos 2 \pi t$
and $|r'(t)|=\sqrt {( -\pi \sin \pi t)^2+(2)^2+(2 \pi \cos 2 \pi t)^2}dt$
$L=\int_{0}^2(\sqrt {( -\pi \sin \pi t)^2+(2)^2+(2 \pi \cos 2 \pi t)^2}dt) dt$
As per question, we will use calculator to find the length of the curve.
Hence, $L= 10.3311$
