HP 15c - Manual (Page 47)

Section 2: Working with f 47
Transformation of Variables
In many problems where the function changes very slowly over most of a very wide interval
of integration, a suitable transformation of variables may decrease the time required to
calculate the integral.
For example, consider again the integral
.



0
dx xe x
Let 3 u e x  
Then u x ln 3
 
And
u
du
dx 3
 
.
Substituting,

 







 




0
1
2
0
0
3
ln 9
3 ) )( ln 3 (
du u u
u
du
u u dx xe
e
e
x
Key in a subroutine that evaluates the function f(u) = 9u
2
ln u.
Keystrokes Display
|¥ 000- Program mode.
´b3 001-42,21, 3
|N 002- 43 12
® 003- 34
|x 004- 43 11
* 005- 20
9 006- 9
* 007- 20
|n 008- 43 32
Key in the limits of integration, then press ´ f 3 to calculate the integral.
Keystrokes Display
|¥
Run mode.
1
v 1.000 00 Keys in lower limit of integration.
0 0 Keys in upper limit of integration.
´f3 1.000 00 Approximation to equivalent integral.
® 3.020 -04 Uncertainty of approximation.