Mathematics

Problem

The curve given in polar form by

r=4\sin\theta

for

0\le \theta \le \pi

is rewritten parametrically as

x=r\cos\theta

and

y=r\sin\theta

. Which definite integral represents the length of the curve on this interval? a)

\displaystyle \int_{0}^{\pi/2} \sqrt{(4\sin\theta)^{2}+(4\cos\theta)^{2}}\,d\theta

\displaystyle \int_{0}^{\pi} \sqrt{(4\sin\theta)^{2}+(4\cos\theta)^{2}}\,d\theta

\displaystyle \int_{0}^{\pi} \big[(4\sin\theta)^{2}+(4\cos\theta)^{2}\big] \,d\theta

\displaystyle \int_{0}^{\pi} \sqrt{(4\cos\theta)^{2}}\,d\theta