WP 34S on DM 42 integral fail

04122022, 07:06 PM
Post: #1




WP 34S on DM 42 integral fail
When integrating from 2 to 3 the function 1/3Root(x), my WP 34S comes up with 0. The answer should be ~.739. I use an 8 size stack and full precision. My code is LBL ‘F0’, FILL, 3Root(x), (1/x), RTN


04122022, 07:20 PM
Post: #2




RE: WP 34S on DM 42 integral fail
Of course, if I break it into 2 integrals, from (2 to 0) + from (0 to 3), I come up with the correct result quickly. I am curious as to why the WP 34S could not deal with using the 2 to 3 domain, and if this is unexpected.


04122022, 09:57 PM
Post: #3




RE: WP 34S on DM 42 integral fail
I guess it has something to do with the discontinuity between the bounds.
— Ian Abbott 

04122022, 11:35 PM
Post: #4




RE: WP 34S on DM 42 integral fail
My TI30X Pro had no problem with the integration, did not require breaking the integral into two…


04132022, 12:38 AM
Post: #5




RE: WP 34S on DM 42 integral fail
My TI89 and HP Prime (IOS App) provided the correct answer just fine. My Casio fx991EX and fxCG50 both gave a Math Error.


04132022, 12:52 AM
Post: #6




RE: WP 34S on DM 42 integral fail
From xrom/integrate.wp34s:
Quote://  the double exponential method relies on the function to be In this specific case you can just integrate from 2 to 3. Also you can skip the FILL command in your program. 

04132022, 03:51 AM
Post: #7




RE: WP 34S on DM 42 integral fail
Re Steve…I have been surprised that the CASIO fxCG50 cannot handle discontinuities where an integration would be a finite result. If the discontinuity is at 0 for example, one is forced to use 1*10^12 for a starting point. Also surprised that it cannot handle trig or exponential commands with complex numbers, does not calculate prime factors, does not have a product command to complement the summation capability. Still, and excellent calculator. Really shines with graphing, graphing analysis, fantastic labeling of the x and y axis, Great with regressions and distributions! Fast as well.


04132022, 08:55 AM
Post: #8




RE: WP 34S on DM 42 integral fail  
04132022, 02:28 PM
Post: #9




RE: WP 34S on DM 42 integral fail
Wow! I forgot about this…other nice examples, remedies given as well!


04132022, 04:00 PM
Post: #10




RE: WP 34S on DM 42 integral fail
(04122022 11:35 PM)lrdheat Wrote: My TI30X Pro had no problem with the integration, did not require breaking the integral into two… Maybe it did "break" integral into two (or more pieces), see Adaptive quadrature Example, gaussquad() use adaptive Gaussian quadratures with 15 points. XCas> gaussquad(surd(x,3), x=2..3.) 1.35517995835 

04132022, 05:42 PM
Post: #11




RE: WP 34S on DM 42 integral fail
I’m integrating the reciprocal of your function…this results in an undefined point at x=0.
This produces, if correct, ~.7379 

04132022, 07:38 PM
(This post was last modified: 04172022 11:22 AM by Albert Chan.)
Post: #12




RE: WP 34S on DM 42 integral fail
XCas> gaussquad(surd(x,3), x,2.,3.)
0.739024156625 This work ! But, I would advice split the integral yourself, to be safe. Adaptive scheme may be fooled. (no matter how good it is, it only see sample points) Below is adaptive simpson's scheme to do above integral. Note line 150. It never touched undefined point at x=0 (But, if integral limits changed, say, 2 .. 6, it will hit x=0 dead on) 10 X1=2 @ X3=3 @ E=.0001 20 T=TIME @ X2=(X3+X1)/2 @ CALL F(X1,F1) @ CALL F(X2,F2) @ CALL F(X3,F3) 30 S=(F1+4*F2+F3)*(X3X1)/6 40 CALL SIMPSON(X1,X2,X3,F1,F2,F3,32*E,S) @ DISP S,TIMET @ END 50 SUB F(X,Y) @ Y=SGN(X)*ABS(X)^(1/3) @ STOP 100 SUB SIMPSON(X1,X3,X5,F1,F3,F5,E,S) 110 H=(X5X1)/4 @ X2=X1+H @ X4=X5H 120 CALL F(X2,F2) @ CALL F(X4,F4) 130 H=H/3 @ S1=(F1+4*F2+F3)*H @ S2=(F3+4*F4+F5)*H 140 S3=S1+S2 @ D=S3S @ H=E/2 150 IF H<1.E15 OR ABS(D)<H THEN S=S3+D/15 @ STOP 160 CALL SIMPSON(X1,X2,X3,F1,F2,F3,H,S1) 170 CALL SIMPSON(X3,X4,X5,F3,F4,F5,H,S2) 180 S=S1+S2 >RUN .73902427614 18.76 Update: slightly modified SIMPSON() recurse condition, with following: 40 CALL SIMPSON(X1,X2,X3,F1,F2,F3,30*E,S) @ DISP S,TIMET @ END 150 IF H<15E15 OR ABS(D)<H THEN S=S3+D/15 @ STOP > RUN .73902420507 15.44 The changes is to compare Sharp BASIC translated HP71B code speed. 

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