Question

Find the exact arc length of the curve

x = cos 3t, y = sin 3t ;(0 ≤ t ≤π)

Answer 1

$L=\int \sqrt{(x')^2+(y')^2}dt$

$x'=-3sin3t, y'=3cos3t$

$L=\int^{\pi}_0 \sqrt{(-3sin3t)^2+(3cos3t)^2}dt=3\int^{\pi}_0 dt=3\pi$