A single arch of a cycloid is defined parametrically by and for

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

Problem

A single arch of a cycloid is defined parametrically by

x(t)=t-\sin t

and

y(t)=1-\cos t

for

0\le t\le 2\pi

. Write the definite integral that gives the length of this arch. Do not evaluate.