Let f and g be the functions given by f(x) = ¼ + sin(Pi*x) and g(x) = 4^ -x. Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of f and g, and let S be the shaded region in the first quadrant enclosed by the graphs of f and g.
a) Find the area of R.
b) Find the areas of S.
c) Find the volume of the solid generated when S is revolved about the horizontal line y= -1.
This shows how to find area of regions and volume of a solid using calculus.