area under the curve

David Kirschtel dkirscht at moose.uvm.edu
Wed Apr 26 10:06:06 EST 1995

J-F Neron (jfneron at fse.ulaval.ca) wrote:
>Is it possible to measure the area under the curve with excel or with some
>MACINTOSH shareware.
>This is a example of the data:

>Time   TG
>-15     80
>0       85
>5       220
>10      210
>15      200


There are a number of numerical integration techniques that would allow 
you to do this and could be adapted to a spreadsheet. The simplest is 
referred to as the Trapezoid Rule (may also be referred to as Eulers Method
in some books) which calculates the area of a trapezoid bounded by 
adjacent sampling points:

  sum across sampling intervals Area= 1/2*[TG(i-1) - TG(i)]*[t(i-1) - t(i)]  

A more accurate and and slightly more complex method is Simpsons Rule 
which fits a parabolic curve across three adjacent points (Best to cruise 
through a Calculus text to get this one).

Also there are the Runge-Kutta algorithms but I don't think these will 
readilty conform to a spreadsheet.

Hope this helps

David Kirschtel               |
Dept. of Botany               |     What if the 'invisible hand' is 
Univ. of Vermont              |
Burlington, VT 05405-0086     |         guided by myopic eyes.
tel   802.656.0429            |
email dkirscht at moose.uvm.edu  |


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