MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions
Problem
Let the curve be given by r=2θ for 0≤θ≤π.
(a) Determine dθdr.
(b) Write—but do not yet evaluate—the definite integral whose value equals the length of the curve on the stated interval.
(c) Evaluate the integral in part (b) to obtain an exact expression for the length. Then approximate this length to three decimal places.