# What is the arclength of the polar curve #f(theta) = sin(3theta)-4cot6theta # over #theta in [0,pi/4] #?

The arclength is infinite.

From the reference Arc Length with Polar Coordinates

Substituting into the integral:

This integral does not converge.

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The arclength of the polar curve f(θ) = sin(3θ) - 4cot(6θ) over θ in [0, π/4] is approximately 0.774.

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