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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 chain lying on the ground is 10 m long and its mass is 80 kg. How much work is required to raise one end of the chain to a height of 6 m?

$$

1411.2 \mathrm{J}

$$

Applications of Integration

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Oregon State University

University of Michigan - Ann Arbor

Boston College

okay before this question to establish agreement Cell Well, first to figure out the wait for links in the chain. And then we can say this is some the vapor leads off the chain and over women some it's gonna be limits. So this quantity times thanks I and that stands for the ice seven total. Okay, But how to calculate the with violence that equals two mg, the mass times the gravity over the both of the road. And that's 80 times 9.8 over 10. And that's equals to the tables, too. 78 1 for Newman, her meter and hangs and his other rivers. Some is gonna be limits and ghostly ability I from one to in 70 April. For those eggs, sums exploit that as exchange in distance and better definition. From this sum, the 1st 1 in the world is 1st 1 0 to 6. Send one for some of the 8.4. Asks the eggs and that's, um 101,471 to Jule. That's it.

University of Illinois at Urbana-Champaign

Applications of Integration