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

[C W]

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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