A trough is 5 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of https://webwork.math.uga.edu/webwork...8eecab29c1.png from https://webwork.math.uga.edu/webwork...23640869f1.png to https://webwork.math.uga.edu/webwork...9a70c4f3b1.png . The trough is full of water. Find the amount of work in foot-pounds required to empty the trough by pumping the water over the top. Note: The weight of water is https://webwork.math.uga.edu/webwork...61007b55c1.png pounds per cubic foot.

I know this problem could be solved by

Work = density * weight * distance traveled by the center of the mass.

I'm having trouble finding the weight. I'm not sure if i should

$\displaystyle int from 0 to 16 x^2 dx$

please help