I am trying to solve a problem dealing with applying integrals to physics. Here's one that I am having trouble with: A trough is 4 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of x^6 from x = -1 to 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: The weight of water is 62 pounds per cubic foot. Here's my attempt at it: I drew an x axis which starts at the top (and at the center) of the trough. Volume of a small slice (horizontal slice): Length * Width 4 * 2(-x+1)^(-1/2)dx Weight (Force) of a small slice (horizontal slice): Volume * Density (4 * 2(-x+1)^(-1/2)dx)*62 Work required for small slice: Force * Distance ((4 * 2(-x+1)^(-1/2)dx)*62)x And then I took the integral of that between 0 and 1 and it did not work. Any ideas?