Transformation Of Variables - HP -15C Advanced Functions Handbook

54 Section 2: Working With [W\s Display
[TsTl 5.328 -04
RCL 2 +
2.000
1.000
00
00
2.598 -04
Returns approximation
and its uncertainty to the
X- and Y-registers,
respectively, before
summing them in
statistical storage
registers.
Sums approximation and
its uncertainty.
Integral over total
interval (0, 228) (recalled
from R
3
).
Uncertainty of integral
(from R
5
),
Transformation of Variables
In many problems where the function changes very slowly over
most of a very wide interval of integration, a suitable transfor-
mation of variables may decrease the time required to calculate the
integral.
For example, consider again the integral
I xe
x
dx .
e~
x
- u
3
.
x = -3 In u
du
dx = -3 .
u
Let
Then
and
Substituting,
f °
=J 9u
2
ln
(-3 In
udu
Key in a subroutine that evaluates the function /(w) = 9u
2
ln u.