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[Phys-L] numerical methods

Hi Folks --

This is relevant to measuring radioactive decays ... and to
many other things. Very very many.

Consider the definite integral of exp(-a t) dt from t1 to t2.
Here is the "textbook" answer:

Now explain why that is *not* the formula that I use in
my software.

What is the smart way of doing it?

I'll post my answer tomorrow, if nobody nails it before then.

The usual jsd puzzle rules apply. Everything I've said is true
to the best of my knowledge. Probably even helpful. No word
games. There are undoubtedly more than one right answer, but
I expect everybody will agree my answer is as good as any,
and vastly better than the "textbook" answer.