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Homework Help: Midpoint and Trapezoidal Rule (EASY)

  1. Apr 11, 2010 #1
    I am solving a sample test for my test on monday, this is the question:

    Table(1) have results from applying the midpoint and trapezoidal rule on 2, 4 and 8 panels

    npanels....midpoint.......trapezoid
    2...........2.19998820...2.48452890
    4...........2.26805993...2.33225855
    8...........2.28422520...2.30015924

    1) do these number support the claim that integrand is concave down? Why?

    2) Calculate the value of Simpson's rule using 8 panels.

    3) what is the minimum number of function evaluations needed to calculate Simpson's rule from scratch on 8 panels?

    ************************

    # 2 is easy: is 2/3(midpoint)+1/3(trappezoid)

    Please help me with the other ones.

    Thanks
     
  2. jcsd
  3. Apr 11, 2010 #2

    berkeman

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    Staff: Mentor

    Please show us more of your work, per the PF Rules for schoolwork.
     
  4. Apr 11, 2010 #3
    there is nothing else to show
     
  5. Apr 11, 2010 #4

    berkeman

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    Staff: Mentor

    Have you actually read the PF rules?
     
  6. Apr 11, 2010 #5
    I have, but I don't understand your question. There is nothing else to show, there is no math involve on the other two steps. You or someone that knows what they are doing, should be able to answer question 1 and 3 by looking at the data.

    You want more work

    2) 2/3(2.28422520)+1/3(2.30015924)=2.28954

    Happy?

    Thanks, I just need some guidance or someone that can answer this simple question.
     
  7. Apr 11, 2010 #6

    berkeman

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    Staff: Mentor

    No, sorry. That doesn't help me. Part of the problem is that I don't understand what you are asking. If you could provide more details and background information, that would be a bit help. What is the "trapezoidal rule" that you are referring to? how does it apply to the numbers that you posted?

    I'm not trying to be a pain here, but honestly, it would help if you posted a lot more background info, and lead us more into helping us provide hints to what you don't understand.
     
  8. Apr 11, 2010 #7
    well, that how the question is written on the sample test.

    midpoint
    http://www.youtube.com/watch?v=fKtSR0_xf5g"
     
    Last edited by a moderator: Apr 25, 2017
  9. Apr 12, 2010 #8
    Your extract from wikipedia is too algebraic for me. If you were to sketch the two cases: (1) concave down and (2) concave up, and draw on each the interpretation of the mid-point and trapezoidal rules, you might then see a way to answering the question.
     
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