# Thread: Find the work done

1. ## 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.

2. 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 ... $dy$

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