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Math Help - Expressing work as a riemann sum

  1. #1
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    Expressing work as a riemann sum

    I've attached a picture of the problem I'm working on. Now I know work is either force times distance or the integral from a to b of f(x)dx, and that F=kx, but it seems like with the information they give me in this problem there isn't enough to find any of the three!

    I AM new to this type of problem and my professor kind of brushed over the topic very quickly so I don't feel very confident in it, if someone could point me in the right direction on one or two of these problems I think I'd be OK to do the rest myself. Thanks in advance!
    Attached Thumbnails Attached Thumbnails Expressing work as a riemann sum-picture-1.png  
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  2. #2
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    OK, I solved the first part of the problem that I posted, but I've attached a problem directly related to the first. It's asking how much work would be done pulling the rope HALF the distance as the first situation. I don't understand why all the answer choices involve adding integrals when really you could just divide your former answer in half?

    Could someone help me out?
    Attached Thumbnails Attached Thumbnails Expressing work as a riemann sum-picture-3.png  
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  3. #3
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    Sorry, I posted a poor picture, here's the right one
    Attached Thumbnails Attached Thumbnails Expressing work as a riemann sum-picture-4.png  
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