# [R] Why two curves and numerical integration look so different?

William Dunlap wdunlap at tibco.com
Thu Feb 11 06:31:10 CET 2016

```Most of the mass of that distribution is within 3e-100 of 2.
You have to be pretty lucky to have a point in sequence
land there.  (You will get at most one point there because
the difference between 2 and its nearest neightbors is on
the order of 1e-16.)

seq(-2,4,len=101), as used by default in curve, does include 2
but seq(-3,4,len=101) and seq(-2,4,len=100) do not so
curve(..., -3, 4, 101) and curve(..., -2, 4, 100) will not show the bump.
The same principal holds for numerical integration.

Bill Dunlap
TIBCO Software
wdunlap tibco.com

On Wed, Feb 10, 2016 at 6:37 PM, C W <tmrsg11 at gmail.com> wrote:

> Dear R,
>
> I am graphing the following normal density curve.  Why does it look so
> different?
>
> # the curves
> x <- seq(-2, 4, by=0.00001)
> curve(dnorm(x, 2, 10^(-100)), -4, 4)  #right answer
> curve(dnorm(x, 2, 10^(-100)), -3, 4)  #changed -4 to -3, I get wrong answer
>
> Why the second curve is flat?  I just changed it from -4 to -3.  There is
> no density in that region.
>
>
> Also, I am doing numerical integration.  Why are they so different?
>
> > x <- seq(-2, 4, by=0.00001)
> > sum(x*dnorm(x, 2, 10^(-100)))*0.00001
> [1] 7.978846e+94
> > x <- seq(-1, 4, by=0.00001) #changed -2 to -1
> > sum(x*dnorm(x, 2, 10^(-100)))*0.00001
> [1] 0
>
> What is going here?  What a I doing wrong?
>
> Thanks so much!
>
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>
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