HP HP-15C

Section 2: Working With [7[j
57
Although the branch for u — 1 adds four steps to your subroutine,
integration near x = 0 becomes more accurate.
As a second example, consider the integral
The derivative of the integrand approaches °° as x approaches 0, as
shown in the illustration below. By substituting x = u2, the
function becomes more well behaved, as shown in the second
illustration. This integral is easily evaluated:
(u
Inu
\du.
Don't replace (u + l)(u — 1) by (u2 — 1) because as u approaches 1,
the second expression loses to roundoff half of its significant digits
and introduces to the integrand's graph a spike near u = l.
0.1 +
As another example, consider a function whose graph has a long
tail that stretches out many, many times as far as the main "body"
(where the graph is interesting)—a function like
f(x) = or g(x) =
x2 +10-10'