Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Upper and Lower Sums

  1. Nov 4, 2013 #1
    I am really having trouble understanding how upper and lower sums are calculated. In the equations Ʃf(Mi)Δx and Ʃf(mi)Δx, what do Mi and mi represent?
     
  2. jcsd
  3. Nov 4, 2013 #2

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It's easiest to understand if you look at a picture. In the figure below (shamelessly borrowed from elsewhere via Google Images), the pink rectangles represent the upper sums and the green rectangles represent the lower sums.

    In other words, the ##M_i## are the heights of the taller (pink + green) rectangles, and the ##m_i## are the heights of the shorter (green only) rectangles.

    How are the heights determined? Quite simple. Each tall rectangle is exactly as high as the maximum value of the function within the width of the rectangle. Each short rectangle is exactly as high as the minimum value of the function.

    fFUOJ.png
     

    Attached Files:

  4. Nov 4, 2013 #3

    pwsnafu

    User Avatar
    Science Advisor

    No. ##M_i## are the x values such that ##f(M_i)## are the heights of the taller rectangles. Similarly for ##m_i##.
     
  5. Nov 4, 2013 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You're correct of course, but that is such unusual notation it makes you wonder if the OP copied the expression correctly from his text.
     
  6. Nov 4, 2013 #5

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Oh, weird. You're right. I misread the question to say what it would have said in most books.
     
  7. Nov 5, 2013 #6
    I did copy them from my text. I wasn't sure how else to go about this.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Upper and Lower Sums
  1. Lower and upper sums (Replies: 6)

  2. Upper and Lower Limits (Replies: 5)

Loading...