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Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it.

A cable that weighs 2 lb/ft is used to lift 800 lb of coal up a mine shaft 500 ft deep. Find the work done.

$6.5 \times 10^{5}$

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 4

Work

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again. The work we're going to calculate equals two parts the work done by the cable, plus the work, then on coal. So for the cable part W one equals two 0 to 400 two x dx. The thing is, we're gonna think of a little segment. The thin slice of the cable and the work done on the simple segment equals to two x times Delta X, and we transform this ribbon son to over Riemann Integral have this results and for double too, because all the call is concentrated at the end of the rope. So it's simply the weight to coal some of the work. This is all the calls going to travel. Imagine the picture, please. That's the cable and physical. So, um, the work, the work that's done on the coal equals two the weight. 800 times. Distance 100. So we're W W 1 22 which is going to be 6.5 times 10 to the five. The total work

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