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## Homework Statement

Find the arc length of polar curve 9+9cosθ

## Homework Equations

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

chain rule..?

(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?