# Thread: Area under a curve without a function

1. ## Area under a curve without a function

I need to find the area between a curve and a straight line. However, I do not have the formula for the curve. Further the curve is not likely to be a specific function because it was generated by a human's arm movement. I just have 100 x,y coordinate points that make up that curve and the 100 x,y coordinates that make up the line.

I was thinking I could create 99 "boxes" (For example use the first two data points of the line and the first two data points of the curve as the corners of the box) then find the area of each box and add these areas together.
Would this be appropriate? or is there a better approach?

2. If you plug those points into your graphing calculator, you can run linear and exponential regression respectively for the two sets of points. Then, find the area using the functions provided by your calculator.

3. Thank-you for the suggestion. Unfortunately, I need a solution that I can do in Excel. I have over 8000 curves that I need to make this calculation for. I can get functions for linear and polynomial curves in Excel but neither fit my data.

4. You have 8000 functions/groups of points or individual points? If you can make the determination of which is on top- the line or the curve, you can eliminate all points on the curve that extend beyond the bounded area between the two functions if that helps.

5. It looks to me like a numerical integration, using, say, Simpson's rule, would work here.

6. I have 8000 groups (of 100 points each). I need to include all of the points within each group because I want to calculate the exact area under the curve for all of the points,regardless of what kind of curve the create. Many of the points make curves, but others can be more chaotic for example angling leftward before curving rightward. So I need a method that will work for many different kinds of "curves".
I am not sure how I could implement the Simpson rule without knowing the equation of the curve. However, I am not very familiar with this rule.