where F(xk) is the force acting at some point in the kth subinterval. We then use the FTC to get
If the force is given in pounds and the distance in feet, then the work is given in foot-pounds (ft-lb).
Problems typical of those involving computation of work are given in the following examples.
EXAMPLE 17
Find the work, W, done by a force F, in pounds, that moves a particle along the x-axis from x = 4
feet to x = 9 feet, if
SOLUTION:EXAMPLE 18
A cylindrical reservoir of diameter 4 feet and height 6 feet is half-full of water weighing w pounds
per cubic foot (Figure N8–3). Find the work done in emptying the water over the top.
SOLUTION: The volume of a slice of water is ΔV = πx^2 Δy, where x = 2. A slice at height y is
lifted (6 −y) ft.FIGURE N8–3
We used 3 as the upper limit since the reservoir is only half full.† The topic “work” is not specifically included in the Topical Outline, but it is an important application of integration.
EXAMPLE 19
A hemispherical tank with flat side up has radius 4 feet and is filled with a liquid weighing w
pounds per cubic foot. Find the work done in pumping all the liquid just to the top of the tank.