A trough is 6 feet long, 3 feet wide, and 3 feet deep. The vertical cross-section of the trough parallel to an end is shaped like an isoceles triangle (with height 3 feet, and base, on top, of length 3 feet). The trough is to be filled with water (density 62.4 lbs/cubic foot). Find the amount of work to fill up the trough. First give the integrand expressed in terms of h, the terms of the height in feet from the bottom of the trough.