Let R be the region in the first quadrant enclosed by the graph of f(x)=cosx−−−−√, the graph of g(x)= ex, and the vertical line x=π2, as shown in the figure above. (a) Write. but do not evaluate, an integral expression that gives the area of R.

(b) Find the volume of the solid generated when R is revolved about the x-axis.

(c) Region R is the base of a solid whose cross-sections perpendicular to the x-axis are semicircles with diameters on the XY-plane. Write, but do not evaluate, an integral expression that gives the volume of this solid.