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    volume of solid revolving by cylindrical shell method

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    Let f and g be the functions given by f(x) = 1 + sin(2x) and 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.

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    The solution is comprised of detailed solution of finding the volume of solid revolving by cylindrical shell method.