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Midpoint Rule Confusion

  1. Feb 11, 2009 #1
    1. The problem statement, all variables and given/known data
    I'm working on a practice test and got stuck on the question: Approximate the length of the curve y=√x, 0≤x≤1 by the midpoint rule with n=4 and ∆x=0.25.


    2. Relevant equations
    Is the midpoint rule the same thing as Simpson's rule? I don't remember going over the midpoint rule in class and I can't find it in the book. If it isn't the same as Simpson's rule, what is it?
     
  2. jcsd
  3. Feb 11, 2009 #2

    Mark44

    Staff: Mentor

    I would guess that in finding the length of a curve by the midpoint rule, you calculate the function value at the midpoint of each subinterval, and then calculate the lengths of those line segments that join those points. For the approximate arc length, just add those lengths together.
     
  4. Feb 11, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    No, the midpoint rule is not the same as Simpson's rule. With Simpson's rule, you approximate the curve by a series of parabolas through each set of 3 points.

    As Mark44 says, the midpoint rule uses the midpoint of each interval to compute the height of a rectangle on that interval.
     
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