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Math Help - Help computing integral involving u-substitution

  1. #1
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    Help computing integral involving u-substitution

    This problem has already been worked out for me, and I understand most of what is going on, but there is one part of it that I am confused about and not sure where exactly it came from. This is the problem:

    Compute the following integral showing your work including the appropriate antiderivative. Hint: The final answer should be an integer.

    ∫[from 4 to 9] 2/((sqrt of y)*(1-sqrt of y)^2) dy

    Solution:

    Step 1: u=1- sqrt of y
    du=-1/(2*sqrt of y) dy

    Step 2: y=4-->u=-1
    y=9-->u=-2

    Step 3: ∫[from -1 to -2] -4/u^2 dy

    Step 4: 4/u |(from -1 to -2)
    =(4/-2) - (4/-1) = 2

    I pretty much understand everything that is going on in this problem except for the third step. I can't seem to figure out where the -4 came from. If anyone could explain to me where the -4 came from or how you would go about getting it, I would greatly appreciate it. Thanks in advance to anyone who can help.
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  2. #2
    MHF Contributor
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    I'm a little confused on your notation, but I think the -4 comes from the 2 in the original integral divided by the -1/2 that is the coefficient for du. So 2/-.5 = -4. That's what it seems like to me.

    edit: your notation is fine. I'm just getting used to reading Latex and all the parentheses throw me off.
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