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

from

to

. 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

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