# GPS, irregular area under graph project

• kvon989
In summary, the conversation revolves around solving a calculus problem involving a GPS track project. The person is trying to find the area under the curve of MPH and Time to determine the distance traveled. They have considered separating points, finding lines of best fit, and using Riemann sum or a modification of it. The data is saved in an excel file and the accuracy of the area calculation is uncertain.
kvon989
Hello,

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.

Thanks

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• Screen Shot 2012-03-19 at 4.23.33 PM.png
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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

It is an excel file, I will try this now.

How accurate will the area be?

## 1. What is GPS?

GPS stands for Global Positioning System, which is a network of satellites and ground stations that provide location and time information to GPS receivers on Earth.

## 2. How does GPS work?

GPS works by using trilateration, which measures the time it takes for signals to travel from satellites to a receiver on Earth. By receiving signals from at least 4 satellites, a GPS receiver can determine its location, speed, and time.

## 3. What is an irregular area under a graph?

An irregular area under a graph is a measurement of the space or region enclosed by a line or curve on a graph that does not have a defined geometric shape, such as a rectangle or triangle.

## 4. How can GPS be used to measure an irregular area under a graph?

GPS can be used to measure an irregular area under a graph by taking multiple GPS coordinates at different points along the perimeter of the irregular area. These coordinates can then be used to calculate the distance between each point and determine the total area enclosed.

## 5. What are some applications of using GPS to measure an irregular area under a graph?

Some applications of using GPS to measure an irregular area under a graph include land surveying, environmental monitoring, and urban planning. It can also be used in agriculture to measure crop yields and in transportation to calculate distances traveled.

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