Re: Why does the TI-85 do...
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Re: Why does the TI-85 do...
Hello Kasper.
The thing you have observed is not a defect of the calculator, but rather a
common phenomenon when you try to compute numerically an integral with
infinite limit(s) of integration.
The function e^(-x^2/2) decreases very fast as x gets away from zero. On the
interval [-E99, 0] the function is a machine zero almost everywhere. The
calculator is evaluating the integral by sampling values of the function at
points inside the interval. The non-zera values form a tiny part at thr right
end, and somehow get missed.
When dealing with integrals like this, it is wise to replace infinity with a
moderate number. For example, if your t>-5, the integral
fnint(e^(-x^2/2),x,-10,t)
can be used, and will give you the right answer up to the last digit
representable on the calculator.
For this particular integral, there is also another way around. It is known
that
fnint(e^(-x^2/2,x,-ifinity,0)=sqrt(pi/2)
Thus, the integral you want to compute is equal to
sqrt(pi/2)+fnint(e^(-x^2/2),x,0,t)
Hope this helps.
Greetings,
Erika
In article <6hq3ch$9ee$1@news1.tele.dk>,
"Kasper Vibe Grevsen" <kaspervg@hotmail.com> wrote:
>
> Hi everybody, does some of you know how to integrate
>
> e^-(0.5x^2) from -infinity to t by hand or by calculator?
>
> When I type in fnInt(e^(-0.5x^2),x,-e99,t) I get 0 for every value of t.
> Why?
> My calculator is in floating point mode, tolerance set to e-5 and delta to
> 0.01. My ROM version is 8.0 however the problem occurs on ROM 10.0 machines
> too.
>
> Does anybody know of a program for the calculator or my PC, which you could
> use to check if some material is e.g. normal distributed? A program (or
> add-in to Excel) which can save all the tiresome drawing by hand on
> distribution paper?
>
> Kind regards Kasper Vibe Grevsen, Denmark
>
>
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