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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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