A trough is 8 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^2 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.
Okay so for the first one, I got as far as slab has volume = 8 [ 2x dy ] = 16 √y dy , y in [0,1] , force = 62 volumes ; distance moved is [ 1 - y ], but I think I keep doing it wrong. I'm not sure how tp continue