Let and for . Which integral represents the arc length of this curve on the given…

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

Problem

Let

x=\sin t

and

y=\cos t + t

for

0\le t \le \pi

. Which integral represents the arc length of this curve on the given interval? (a)

\displaystyle \int_{0}^{\pi} \sqrt{(\cos t)^{2}+(\sin t + 1)^{2}}\,dt

(b)

\displaystyle \int_{0}^{\pi} \sqrt{(\cos t)^{2}+(-\sin t + 1)^{2}}\,dt

(c)

\displaystyle \int_{0}^{\pi} \sqrt{(\cos t)^{2}+(-\sin t)^{2}}\,dt

(d)

\displaystyle \int_{0}^{\pi} \sqrt{(\cos t)^{2} + (\cos t + t)^{2}}\,dt