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Find the volume of the solid generated by revolving the region about the given line. The region in the first quadrant bounded above by the line y = 2/3, below by the curve y = csc xcot x, and on the right by the line x = π/2, about the line y = 2/3. Set up the integral that gives the volume of the solid. (Type exact answers, using π as needed.) The volume of the solid generated is cubic units. (Type an exact answer, using π as needed.)

Find the volume of the solid generated by revolving the region about the given line. The region in the first quadrant bounded above by the line y = 2/3, below by the curve y = csc xcot x, and on the right by the line x = π/2, about the line y = 2/3. Set up the integral that gives the volume of the solid. (Type exact answers, using π as needed.) The volume of the solid generated is cubic units. (Type an exact answer, using π as needed.)

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Find the volume of the solid generated by revolving the region about the given line. The region in the first quadrant bounded above by the line y = 2/3, below by the curve y = csc xcot x, and on the right by the line x = π/2, about the line y = 2/3. Set up the integral that gives the volume of the solid. (Type exact answers, using π as needed.) The volume of the solid generated is cubic units. (Type an exact answer, using π as needed.)

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