# [R] Equation of a curve

Greg Snow 538280 at gmail.com
Thu Apr 3 23:22:18 CEST 2014

```The mean value theorem of integration (I have a cross-stitch of this
theorem hanging on my wall (between cross-stitches of the central
limit theorem and Bayes theorem)) tells us that the area under a curve
is equal to the width of the area of interest times the average height
of the curve.  Often when we want to use the area under a curve in
statistics we can just use the average of the y-values generating the
curve and it is much simpler.

If the x-coordinates of your points are evenly spaced or are random
with a fairly uniform distribution then the mean height of the points
will probably be as useful as any curve that you computed and then
integrated.

If the x-coordinates are not uniformly spread then you may benefit
from a weighted average.  One option for estimating the integral is to
use the trapezoidal rule or Simpson's rule, but if you look at those
formulas, they are just a weighted average of the heights again.

So, while Yes, R can estimate curves and compute numerical integrals
of the curves, there is a good chance that you don't really need to do
either.

On Thu, Apr 3, 2014 at 9:26 AM, Frances Cheesman <fcheesman.fc at gmail.com> wrote:
> Hi all,
>
> I have a number of bacterial growth curves I would like to find the
> equations for these and then integrate them to find the area under the
> curves for me to do stats on later.
>
> Is there any way I can do this in R?
>
> Thanks,
>
> Frances
>
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>
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