HP42s first major program (Double Integral) Best way to approach?

[Ángel Martin]

(05-27-2020 03:46 AM)Paul Dale Wrote:  Could the 15C do double integrals?
I don't have a 15C nearby to check...

I very much doubt it, neither does INTEG in the Advantage Pac - which is supposed to be a direct port from the 15C, or at least based on it. When you try it presents the RECURSION error message.

However recursive integrals are supported by FITG2 in the Advantage_Math ROM, which uses FINTG from the SandMath directly with a custom trick played on the INTEG buffer to allow dual existence while the inner integral is being calculated. Manual is available here, look for ADVG in the listing.

For this example the instructions are:

type "FN" in ALPHA
24, ENTER^, 29 ENTER^, 0, ENTER^, 12
XEQ "FITG2" with the desired accuracy in display mode.

With FIX 4 I get 581.4058 - which agrees with the given answer when multiplied by four.

the integrand function is as follows: inner integral is dx and outer integral is dr
On entry, the Inner variable is in the stack (four levels)
and the Outer variable is in R01

Code:

01 LBL "FN"
02 RCL 03
03 X^2
04 X<>Y  
05 X^2
06 -
07 SQRT
08 RCL 01
09 *
10 RCL 01
11 X^2
12 RCL Z
13 X^2
14  -
15 SQRT
16 /
17 END