Integral and the trough prb!

A trough is http://webwork.math.uwyo.edu/webwork...a3da5aab21.png feet long and http://webwork.math.uwyo.edu/webwork...6774a851b1.png foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of http://webwork.math.uwyo.edu/webwork...467ce0c5a1.png from http://webwork.math.uwyo.edu/webwork...23640869f1.png to http://webwork.math.uwyo.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 http://webwork.math.uwyo.edu/webwork...61007b55c1.png pounds per cubic foot.

I drew a picture thats about as far as I could get.