## calculus 2: work prob.

I really need help with this problem.

the fuel tank on a truck has trapezoidal cross sections with dimensions (in feet) shown in the figure. assume that an engine is approximately 3 ft. above the top of the fuel tank and that diesel fuel weighs approximately 53.1 pounds per cubic foot. find the work done by the fuel pump in raising a full fuel tank to the level of the engine. the graph looks like half of this:

bottom base 1ft by 3ft
top base 3ft by 2ft
height of 3 ft.

so far i have the distance: (3-y)
weight: 51.3 X 3 ft.

i also found X= (2y/3)^2
but im not sure if it is right or what varialbes i need also i cant seem to figure out form what to what i am integrating 0 to 8?