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GPS, irregular area under graph project

  1. Mar 19, 2012 #1

    I am trying to solve a calculus problem, and do not know quite how to approach it.
    I am doing a project on a GPS track, I have mapped out an area with GPS, the GPX file gives speed, lat, long, time and some other data. I am comparing the area under the curve of MPH(Y axis) and Time(hrs X-axis) with the arc length of the traveled path compared to actual distance traveled via car odometer.

    I have completed the data gathering, and am having difficulties approaching the graph, and finding the area under the curve to find the distance.

    The Graph is attached.

    My approaches:

    1. Separate the points and find the area under each and every 2 points
    Although this would work, it would take me a very long time.

    2. Finding lines of best fit, possibly splitting up the graph into multiple sections and finding lines of best fit, but they again, the accuracy would not be the greatest.

    3. Using Reimons sum or a modification of it.

    Note: Their are 203 points...

    Any insight, tips, or suggestions would be extremely helpful.


    Attached Files:

  2. jcsd
  3. Mar 19, 2012 #2


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    How is this data saved? You can do a Riemann sum on your computer fairly easily probably... for example if you have a csv file (or anything else you can open in excel) you have two columns:
    col A is time stamps
    col B is speeds

    for col C entry j is colA(entry j+1)-colA(entry j).
    Then colD(entry j) = colB(entry j)*colC(entry j)
    sum(colD) is a left hand Riemann sum
  4. Mar 19, 2012 #3
    It is an excel file, I will try this now.

    How accurate will the area be?
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