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Homework Help: Finding Lower Sums for a Region

  1. Jan 21, 2010 #1
    1. The problem statement, all variables and given/known data

    FIND THE LOWER SUM FOR THE REGION BOUNDED BY f(x) = 25 - x^2 AND THE X - AXIS BETWEEN x = 0 and x = 5. SOLVE ANALYTICALLY!!

    2. Relevant equations

    None that I'm aware of...

    3. The attempt at a solution

    f(x) = -x2 + 25
    and
    [tex]\Delta[/tex]X = b-a/n = 5-0/n = 5/n



    Here's my question: how do I find the left endpoints in order to solve for the lower sum?
     
    Last edited: Jan 21, 2010
  2. jcsd
  3. Jan 21, 2010 #2
    Okay, here's what I have thus far, and I'm not sure this is correct:


    mi= 5(i-1)/n

    After much sigma notation and algebra...

    eventually ending up with 125/n3 {(n(n+1)(2n+1)/6) - 2[n(n+1)/2] + n}
     
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