The base of a solid is bounded by the functions $f(x)=\cos(x)$ and $g(x)=x^2$. If the cross-sections perpendicular to the $x$-axis are semicircles, what is the volume of the solid?
I solved it by integrating (pi/2)(r)^2 between the bound (-.824,.824) where r is the difference in the two curves f(x) = cos(x) and g(x) = x^2, however I got 1.374, which is incorrect. Can anyone please point out any mistakes I made?