The length of the arc of the curve r = f(θ) between the points, where θ = α and θ = β , is:

• A. \(\mathop \smallint \nolimits_\alpha ^\beta \sqrt {{r^2} + \left( {\frac{{dr}}{{d\theta }}} \right)^2} \;d\theta \;\)
• B. \(\mathop \smallint \nolimits_\alpha ^\beta \sqrt {1 + {{\left( {r\;sin\theta } \right)}^2}} \;d\theta \)
• C. \(\mathop \smallint \nolimits_\alpha ^\beta \sqrt {1 + {{\left( {\frac{{dr}}{{d\theta }}} \right)}^2}} \;d\theta \)
• D. \(\mathop \smallint \nolimits_\alpha ^\beta \sqrt {r + {{\left( {r\frac{{dr}}{{d\theta }}} \right)}^2}\;} \;d\theta \)