Polar Equations - Arc Length Practice Problems Online

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

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

\displaystyle{ \frac{128}{3}\left[ (\pi^2+1)^{\frac{3}{2}} - 2 \right]}

\displaystyle{ \frac{128}{3}\left[ (\pi^2+1)^{\frac{3}{2}} - 4 \right]}

\displaystyle{ \frac{128}{3}\left[ (\pi^2+1)^{\frac{3}{2}} - 1 \right]}

\displaystyle{ \frac{128}{3}\left[ (\pi^2+1)^{\frac{3}{2}} - 3 \right]}

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.

\displaystyle{ \frac{19}{2}\left( 2 + \ln 3\right)}

\displaystyle{ \frac{19}{2}\left( \sqrt{3} + \ln(1+\sqrt{3})\right)}

\displaystyle{ \frac{19}{2}\left( \sqrt{2} + \ln(1+\sqrt{2})\right)}

\displaystyle{ \frac{19}{2}\left( \sqrt{5} + \ln(1+\sqrt{5})\right)}

Polar Equations Calculus