+- HP Forums (https://www.hpmuseum.org/forum)
+-- Forum: Not HP Calculators (/forum-7.html)
+--- Forum: Not quite HP Calculators - but related (/forum-8.html)
+--- Thread: Improper Integrals on 42 platforms (/thread-12237.html)
Improper Integrals on 42 platforms - lrdheat - 01-20-2019 06:48 PM
I was grateful to have been generously given an HP-42S. I was quite impressed, and ordered the DM 42. I'm wondering...has anyone noticed that the 42S and the DM 42 seem to have difficulty with improper integrals? I tried integrating (abs(sin x))/x from -pi/4 to pi/3, and found that even on the DM 42, I had to give up when using acc=1E-5. It did better at acc=1E-03. In contrast, my new TI 30X Pro MathPrint with the default at 1E-05 comes up with an answer good through 5 decimals in 28 seconds. On proper integrals, the various 42's are faster, the DM 42 often very quick. Still, I find that I like the feel of the 42S and it's keyboard. The DM 42 keyboard annoyingly will miss a keystroke from time to time...
RE: Improper Integrals on 42 platforms - Thomas Klemm - 01-20-2019 08:40 PM
I assume that the problem is rather related to the discontinuity at \(x=0\) than the division by \(0\).
You can try to integrate:
\(\int_{-\frac{\pi}{4}}^{\frac{\pi}{3}}\frac{\left |x \right |}{x}dx\)
Use the following program and you will probably have the same experience:
Code:
00 { 15-Byte Prgm }
01▸LBL "f(x)"
02 MVAR "x"
02 RCL "x"
04 SIGN
05 ENDYou can speed things up if you split your integral into two parts:
\(\int_{-\frac{\pi}{4}}^{\frac{\pi}{3}}\frac{\left |\sin x \right |}{x}dx=\int_{-\frac{\pi}{4}}^{0}\frac{\left |\sin x \right |}{x}dx+\int_{0}^{\frac{\pi}{3}}\frac{\left |\sin x \right |}{x}dx\)
I haven't tried this using the HP-42S but it works with the Free42.
HTH
Thomas
RE: Improper Integrals on 42 platforms - Albert Chan - 01-21-2019 05:56 PM
(01-20-2019 08:40 PM)Thomas Klemm Wrote: You can speed things up if you split your integral into two parts:
\(\int_{-\frac{\pi}{4}}^{\frac{\pi}{3}}\frac{\left |\sin x \right |}{x}dx=\int_{-\frac{\pi}{4}}^{0}\frac{\left |\sin x \right |}{x}dx+\int_{0}^{\frac{\pi}{3}}\frac{\left |\sin x \right |}{x}dx\)
Or, remove the discontinuity: integ(sin(x)/x, x, pi/4, pi/3) ~ 0.226483
RE: Improper Integrals on 42 platforms - Csaba Tizedes - 01-21-2019 06:01 PM
(01-20-2019 06:48 PM)lrdheat Wrote: my new TI 30X Pro MathPrintI'll be a little OFF, but could you start a topic for this calculator? I am very interested but not so much information available yet from users.
Thanks,
Csaba
RE: Improper Integrals on 42 platforms - lrdheat - 01-21-2019 08:58 PM
It's an updated 36X Pro, essentially identical, but at least twice as fast, more generous on how many characters can be accepted in a MathPrint mode equation, 3 data lists can handle 50 entries, up from 42 on the 36X Pro. 3 new regressions are available: a*x, a/x + b, a*e^ (b*x). No auto "best choice" as offered by some HP's. Display is easier to read.
RE: Improper Integrals on 42 platforms - ijabbott - 01-21-2019 09:06 PM
(01-21-2019 08:58 PM)lrdheat Wrote: It's an updated 36X Pro, essentially identical, but at least twice as fast, more generous on how many characters can be accepted in a MathPrint mode equation, 3 data lists can handle 50 entries, up from 42 on the 36X Pro. 3 new regressions are available: a*x, a/x + b, a*e^ (b*x). No auto "best choice" as offered by some HP's. Display is easier to read.
And no silver keys!
RE: Improper Integrals on 42 platforms - ijabbott - 01-21-2019 09:14 PM
(01-21-2019 06:01 PM)Csaba Tizedes Wrote:(01-20-2019 06:48 PM)lrdheat Wrote: my new TI 30X Pro MathPrintI'll be a little OFF, but could you start a topic for this calculator? I am very interested but not so much information available yet from users.
Thanks,
Csaba
There are quite a few posts about the Pro MathPrint in the thread TI-36X Pro—Replace the batteries or just get a new one? from post #19 onwards.
RE: Improper Integrals on 42 platforms - lrdheat - 01-21-2019 10:51 PM
Another observation: Many of the constants have been updated on the 30X Pro MathPrint since the 36X Pro...