Area under unknown curve

D

Damian Ouch

Dear Helpers...

I have an area problem.

I need to calculate the area under a curve between any two
limits for which I do not know the equation. Further, the
curve does not exactly obey any standard funtion type
unless its the sum of many and varied restricted functions.

To help you understand my dilema, the problem is in
dealing with physical values related to my materials
behaviour assignement for the Victorian (Australia) year
12 Physics course.

I tested fishing line (2 different lengths), by adding
calibrated masses and measuring the resulting extension
through until failing point.

I have hence tabulated in Excel a lovely sheet of results
for each length of line that gives me instantaneous spring
constant values, stress values, strain values,
instantanous Youngs modulous values and of course the
mass, resulting force and extension values.

From here I was able to plot, for each line length, force
Vs extension and stress vs strain. As you probably know I
now want to be able to find varioius areas under the force
vs extension graphs in order to find elastic potential
energy and various areas under the stress vs strain graphs
in order to find strain energy per unit volume of material.

If I can do this, the assignement is done. I can email to
you the workbook so you can see exactly what I am dealing
with. I am not an excel wizard so anything that is
exceedingly technical may find a brick wall in my
brain...hehe

Please help...

Damian.
 
L

Leo Heuser

Hi Damian

Here's one way to do it:

Assuming X-values in C2:C21 and Y-values in D2:D21
(The more points pr. unit the closer the approximation)

To get an approximation of the area under the curve use this formula:

=SUMPRODUCT((C3:C21-C2:C20)*(D3:D21+D2:D20))*0.5

I have derived the formula from the trapezoid rule for unequally spaced
data.

--
Best Regards
Leo Heuser
MVP Excel

Followup to newsgroup only please.
 
D

Damian Ouch

Thanks Leo.

I'll give that a go. Immediately upon posting the
message, I did think that I could use the trapezoidal
estimate between each data value that I have. I'll give
this a go and see where i get to. Will be sure to post
another message if I fail.

Cheers

Damian
 

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