For the curve given by and on

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

For the curve given by

x(\theta)=\sin\theta

and

y(\theta)=\ln(\cos\theta)

0\le\theta\le\frac{\pi}{4}

, write the definite integral whose value equals the arc length of the curve over this interval. Do not evaluate.