$y = \sin(\pi x), 0 \le x \le 1$
y' = \pi \cos(\pi x)
(y')^2 = \pi^2\cos^2(\pi x)
$ds = \sqrt{1 + \pi^2 \cos^2(\pi x)}$
$r = y = \sin(\pi x)$
$S = \displaystyle\int_0^1 2 \pi\sin(\pi x)\sqrt{1 + \pi^2 \cos^2(\pi x)} dx$
I'm a little lost as to what to do next. Should I have simplified ds more or do I need to do a substitution with $u = \pi^2\cos^2(\pi x)$?