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Riemann sum, a question

  1. Dec 26, 2011 #1
    Let Pn denote the partition of the given interval [a,b] into n sub intervals of equal length Δxi = (b-a)/n
    Evaluate L(f,Pn) and U(f,Pn) for the given functions f and the given values of n.

    f(x)=x on [0,2], with n=8

    2.My solution

    x0 = 0, x1 = 1/4, x2 = 1/2, x3 = 3/4, x4 = 1, x5 = 5/4, x6 = 3/2, x7 = 7/4, x8 = 2

    L(f,Pn) = 1/4(1/4+1/2+3/4+1+5/4+3/2+7/4+2) = 2.25 = 9/4

    U(f,Pn) = 1/4(0+1/4+1/2+3/4+1+5/4+3/2+7/4) = 1.75 = 7/4

    In the answersheet the lower rienmann sum is 7/4 and the upper rienmann is 9/4

    What is wrong ?
     
  2. jcsd
  3. Dec 26, 2011 #2

    LCKurtz

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    The only thing I see that is incorrect is your spelling of "Riemann".
     
  4. Dec 26, 2011 #3

    micromass

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    Shouldn't these two be swapped?? To find L, you take the lowest value in the interval. So it makes sense that

    L(f,Pn) = 1/4(0+1/4+1/2+3/4+1+5/4+3/2+7/4)

    and not the thing you wrote.
     
  5. Dec 26, 2011 #4

    LCKurtz

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    Heh. I didn't even notice that and I was wondering why he said the answers were wrong.
     
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