Let f and g be the functions given by $\displaystyle f(x)=1+sin(2x)$ and $\displaystyle g(x)=e^{x/2}$. Let R be the shaded region in the first quadrant enclosed by the graphs of f and g.

The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from y=f(x) to y=g(x). Find the volume of this solid.

How do I do this problem?