Find the arc length of polar curve 9+9cosθ
L = integral of sqrt(r^2 + (dr/dθ)^2 dθ
dr/dθ = -9sinθ
r = 9+9cosθ
The Attempt at a Solution
1. Simplifying the integral
r^2 = (9+9cosθ^2) = 81 +162cosθ + 81cos^2(θ)
(dr/dθ)^2 = 81sin^2(θ)
r^2 + (dr/dθ)^2 = 81 + 162cosθ + 81cos^2(θ) + 81sin^2(θ)
81sin^2(θ) + 81cos^2(θ) = 81
162 + 162cosθ = r^2 + (dr/dθ)^2
now I have to take the integral of the squareroot...
Integral of sqrt(162 + 162cosθ)dθ
(2/3)(162+162cosθ)^3/2*(162θ + 162sinθ)
Integrated between 0 and 2pi...?
which would lead to a crazy high number that I got as 3957501.966.
Anyone know where I went wrong?