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Calculate the work done to raise a cable

As in the previous exercise we are given a 50 foot cable, weighing 4 pounds per foot. Now, we attach a weight of 50 pounds to the end. Calculate the work required to raise the cable 25 feet.


Since there is a 50 pound weight on the end of the cable the force function is now given by f(x) = 250 - 4x. So, the work required is

    \[ W = \int_0^{25} (250-4x) \, dx = 6250 - 1250 = 5000 \text{ ft-lbs}. \]

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