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 Discussion: All Topics Topic: Improper Integrals Related Item: http://mathforum.org/mathtools/tool/1699/

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 Subject: RE: Improper Integrals Author: LFS Date: Apr 5 2009
Probably not what you had in mind...

Do they know statistics distributions? I like to do demonstrate these with
GeoGebra (freeware) and then prove them with improper/proper integrals.
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I find it very interesting to show that a positive function is a pdf
(probability density functions) if it (improperly) integrates to 1 (full
probability).

Exponential distribution:  f(x)=lambda*exp(-lambda*x) for lambda>1 integrates
from 0 to infinity to 1.  (e.g. lambda = 1.8). Nice easy improper integral.

Here, they can then play with proper integrals too such as: find x so that
Pr(X<x)=1/2 - that is, when do you get half the probability and/or think both
about what this means with probability and/or half-life.

Exponential Polynomial distribution: f(x)=7.5*exp(-3x)-7.5exp(-5x) which
is a typical distribution for "crash time" or "failure".