The parametric equations x= 4 − 5 sin 3t and y = 2 + 5 cos 3t for 0 ≤ t ≤ 𝜋/6 represent a curve C.
Find the length L of the curve C.
L =
L = ∫[0,π/6] √((-15cos3t)^2 + (-15sin3t)^2) dt
= ∫[0,π/6] 15√((cos3t)^2 + (sin3t)^2) dt
= ∫[0,π/6] 15 dt
= 5π/2