Improper Integrals on 42 platforms

01202019, 06:48 PM
Post: #1




Improper Integrals on 42 platforms
I was grateful to have been generously given an HP42S. 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=1E5. It did better at acc=1E03. In contrast, my new TI 30X Pro MathPrint with the default at 1E05 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...


01202019, 08:40 PM
Post: #2




RE: Improper Integrals on 42 platforms
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 { 15Byte Prgm } You can speed things up if you split your integral into two parts: \(\int_{\frac{\pi}{4}}^{\frac{\pi}{3}}\frac{\left \sin x \right }{x}dx=\int_{\frac{\pi}{4}}^{0}\frac{\left \sin x \right }{x}dx+\int_{0}^{\frac{\pi}{3}}\frac{\left \sin x \right }{x}dx\) I haven't tried this using the HP42S but it works with the Free42. HTH Thomas 

01212019, 05:56 PM
(This post was last modified: 01212019 06:01 PM by Albert Chan.)
Post: #3




RE: Improper Integrals on 42 platforms
(01202019 08:40 PM)Thomas Klemm Wrote: You can speed things up if you split your integral into two parts: Or, remove the discontinuity: integ(sin(x)/x, x, pi/4, pi/3) ~ 0.226483 

01212019, 06:01 PM
Post: #4




RE: Improper Integrals on 42 platforms  
01212019, 08:58 PM
Post: #5




RE: Improper Integrals on 42 platforms
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.


01212019, 09:06 PM
Post: #6




RE: Improper Integrals on 42 platforms
(01212019 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! — Ian Abbott 

01212019, 09:14 PM
Post: #7




RE: Improper Integrals on 42 platforms
(01212019 06:01 PM)Csaba Tizedes Wrote:(01202019 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. There are quite a few posts about the Pro MathPrint in the thread TI36X Pro—Replace the batteries or just get a new one? from post #19 onwards. — Ian Abbott 

01212019, 10:51 PM
Post: #8




RE: Improper Integrals on 42 platforms
Another observation: Many of the constants have been updated on the 30X Pro MathPrint since the 36X Pro...


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