Handheld Calculator Evaluates Integrals
Description
by William M. Kahan, in Hewlett-Packard Journal, August 1980 p23 (PDF).
The HP-34C is currently the only one, that can evaluate conveniently integrals of implicit functions, like SOLVE. For example, let v = v(u) be the root of the equation v - u + ln (1 + uveu) = 0
Then ∫01 u du/v(u) = 1.81300 ± 0.000005 after appx. 10 minutes results from a program rather shorter than on any previous calculator.
Program Resources
Labels
| Name |
Description |
|
| A |
Integral u·du/v(u) |
|
| B |
v - u + ln(1 + u·v·e^u) |
|
Storage Registers
| Name |
Description |
|
| I |
Saves u and v |
|
Program
| Line |
Display |
Key Sequence |
|
| 000 |
|
|
|
| 001 |
42,21,11 |
f LBL A |
|
| 002 |
42, 4,25 |
f Χ↔ I |
|
| 003 |
42,10,12 |
f SOLVE B |
|
| 004 |
42, 4,25 |
f Χ↔ I |
|
| 005 |
45 25 |
RCL I |
|
| 006 |
10 |
÷ |
|
| 007 |
43 32 |
g RTN |
|
| 008 |
42,21,12 |
f LBL B |
|
| 009 |
45 25 |
RCL I |
|
| 010 |
20 |
× |
|
| 011 |
43 36 |
g LSTΧ |
|
| 012 |
12 |
eˣ |
|
| 013 |
20 |
× |
|
| 014 |
1 |
1 |
|
| 015 |
40 |
+ |
|
| 016 |
43 12 |
g LN |
|
| 017 |
45 25 |
RCL I |
|
| 018 |
30 |
− |
|
| 019 |
40 |
+ |
|
| 020 |
43 32 |
g RTN |
|