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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 10-ft chain weighs 25 lb and hangs from a ceiling. Find the work done in lifting the lower end of the chain to the ceiling so that it's level with the upper end.

$62.5 \mathrm{ft}-\mathrm{lb}$

Applications of Integration

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Campbell University

University of Nottingham

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Boston College

OK, so first we gonna get that. This is the road them likens to the mass over the length. So that's the, uh wait for with the wicker length, it's 15 and next we're gonna figure out the distance that's moved by a signal of the road. It's gonna tricky here because we haven't noticed that. Uh, see, this is over White ordinance. This is Theo X, and this is zero way zero. That's why ordinance, this is a total height at 10 feet, right? The rope only move for the lower parts of the world have isn't fine. So if you move that you move the road about five is the role. You're not move anyone here. So this is that the robot will travel for a piece of rope announcements or things like baroque. These two cases zero for why, No longer less than five. And Tim as to why, if y listen for so here we have our density we have over. This is the work equals to zero toe l. So this hour l the total length of the height which was to tear love no times worthy way, which is Deacon's to observe to five, 10 months to White Tim's Love, that boy and for what? Within 50 So finally, this equals two, since his 15 feet don't.

University of Illinois at Urbana-Champaign

Applications of Integration