AP Calculus BC / Parametric Equations, Polar Coordinates, and Vector-Valued Functions / Question No. 10

10. The length of the path described by the parametric equations \( x = \sin t + \ln(\cos t) \) and \( y = \cos t \), for \( \frac{\pi}{6} \leq t \leq \frac{\pi}{3} \), is given by

\( \int_{\pi/6}^{\pi/3} \sqrt{\cos^2 t + 2\sin t + 2} \, dt \)

\( \int_{\pi/6}^{\pi/3} \sqrt{\sin^2 t + 2\cos t + 2} \, dt \)

\( \int_{\pi/6}^{\pi/3} \sqrt{\cot^2 t + 2\cos t} \, dt \)

\( \int_{\pi/6}^{\pi/3} \sqrt{\sec^2 t - 2\sin t} \, dt \)

Answer is: option4

\( \int_{\pi/6}^{\pi/3} \sqrt{\sec^2 t - 2\sin t} \, dt \)

Solution:

\( \int_{\pi/6}^{\pi/3} \sqrt{\sec^2 t - 2\sin t} \, dt \)

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Home Practice Questions AP Calculus BC Parametric Equations, Polar Coordinates, and Vector-Valued Functions Question No. 10

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