Find the area of the surface obtained by rotating the curve about the x-axis.
$\displaystyle y = sin\pi x $
0 < x < 1
Where exactly are you stuck? If it's finding the integral, first make the substitution $\displaystyle u = \pi \cos (\pi x)$.
Now make either (not both!!) of the following substitutions
1. $\displaystyle u = \sinh t$ (this is the one I prefer).
2. $\displaystyle u = \tan t$ (more work will be required).