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Math Help - Find the work done

  1. #1
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    Find the work done

    A trough is feet long and foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of from to . 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 pounds per cubic foot.
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  2. #2
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    work = integral of WALT

    W = weight density, 62 lbs/ft^3
    A = horizontal cross-sectional area of a representative "slab" of liquid in terms of y ...
    area = 2x(10) = 20x = 20y^{\frac{1}{6}}
    L = vertical distance to lift a representative "slab" to the top, (1 - y)
    T = "slab" thickness ... dy



    W = \int_0^1 62 \cdot 20y^{\frac{1}{6}}(1 - y) \, dy
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