HP HP-32S - Page 280

FCxJ
ftx)
A
Calculated integral
of this function
will be accurate.
Calculated integral
of this function
may be inaccurate.
In many cases you will be familiar enough with the function you
want to integrate that you will know whether the function has any
quick wiggles relative to the interval of integration. If you're not fa
miliar with the function, and you suspect that it may cause problems,
you can quickly plot a few points by evaluating the function using the
subroutine you wrote for that purpose.
If, for any reason, after obtaining an approximation to an integral,
you suspect its validity, there's a simple procedure to verify it: subdi
vide the interval of integration into two or more adjacent subintervals,
integrate the function over each subinterval, then add the resulting
approximations. This causes the function to be sampled at a brand
new set of sample points, thereby more likely revealing any previ
ously hidden spikes. If the initial approximation was valid, it will
equal the sum of the approximation over the subintervals.
278 D: More About Integration