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Applications of Integrals

  1. Nov 2, 2004 #1
    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?
  2. jcsd
  3. Nov 3, 2004 #2


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    Where did the square roots come from?
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