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## Polar Equations Calculus

Just because your equation is polar doesn't mean you can't do Calculus! Some tricks can extend the toolkit of Calculus to these special equations.

# Arc Length

Find the arc length of the cardioid $$r=8+8\sin \theta.$$

Find the arc length of the curve $$r=16\theta^2$$ for $$0 \le \theta \le 2\pi.$$

Find the arc length of the cardioid $$r=11-11\cos \theta.$$

Find the arc length of the curve $$r=11\sin \theta$$ for $$0 \le \theta \le \pi.$$

Find the arc length of the curve $$r=19 \theta$$ for $$0 \le \theta \le 1.$$

Note: The above figure is not drawn to scale.

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