_{-z}

^{z}exp(-x

^{2}) dx, or more generally numerical integration? Of course as z goes to ∞ this approaches √π, with very small tails. (The link goes to an old post of mine that unfortunately has broken LaTeX; you can read the alt text for the images. The idea is that in∫

_{z}

^{∞}exp(-x

^{2}) dx, the integrand can be bounded above by the exponential exp(-z

^{2}-2xz); integrating this, the original integral is less than exp(-z

^{2})/2z and this is pretty tight. And yes, I know, I should switch to a platform with LaTeX support.)

So you expect to get something near √π for any reasonably large value of z. But if z is large enough -- say 1000 -- then you get a very small value, in this case on the order of 10

^{-7}. Presumably if the range of integration is wide enough, then the integration method used by the calculator doesn't actually pick up the central region where the action is actually happening.

## 3 comments:

I'm using MathJax for math and it works fairly well. Put the snippet from http://pastebin.com/ETPfQuSF right after "head" tag in your blog template (under "Design"/"Edit HTML"), then anything between $ or $$ will render as formulas

On the TI-84 it uses the Gauss-Kronrod quadrature (source)

It's probably the same for the 83+.

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