Calculus in polar coordinates

Question

Find the exact length of the polar curve.

r = 3 cos(𝜃),    0 ≤ 𝜃 ≤ 𝜋

I was only able to get to the below answer:

∫

from 0 to pi. √1+9sin^2(X) dx

Answer 1

r = 3cosθ, 0 ≤ θ ≤ π

Length = L = ∫_{(0 to π)} √ [ r² + (dr/dθ)²]dθ = ∫_{(0 to π)}√[9cos²θ + 9sin²θ]dθ

L = ∫_{(0 to π)}√[9(cos²θ + sin²θ)]dθ = ∫_{(0 to π)}3dθ = 3π

Note: The graph of the given curve is the circle centered at (1.5, 0) with radius 1.5.

So, the arc length is the circumference, C, of the circle. C = 2π(1.5) = 3π.