A trough is 6 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of $\displaystyle {y}={x}^{{{8}}}$ from $\displaystyle {x}=-{1}$ to $\displaystyle {x}={1}$ . 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: In this problem, use 62 pounds per cubic foot as the weight of water.



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