(Solved): ( 3 points) A trough is 6 feet long and 1 foot high. The vertical cross-section of the trough paral ...

( 3 points) 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 $y=x^6$ from $x=?1$ to $x=1$. The trough is full of water. Find the amount of work required to empty the trough by pumping the water over the top. Note: The weight of water is 62 pounds per cubic foot. Your answer must include the correct units. (You may enter $lbf$ or $l{b}^{?}ft$ for $ft?lb.)$