User Manual

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
dxxe
x
Let
3
ue
x


Then
ux ln3
And
u
du
dx 3
.
Substituting,

 












0
1
2
0
0
3
ln9
3))(ln3(
duuu
u
du
uudxxe
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.
1v
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.