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Full Version: Improper Integrals on 42 platforms
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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...
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 END

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 HP-42S but it works with the Free42.

HTH
Thomas
(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
(01-20-2019 06:48 PM)lrdheat Wrote: [ -> ]my new TI 30X Pro MathPrint
I'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
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.
(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!
(01-21-2019 06:01 PM)Csaba Tizedes Wrote: [ -> ]
(01-20-2019 06:48 PM)lrdheat Wrote: [ -> ]my new TI 30X Pro MathPrint
I'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.
Another observation: Many of the constants have been updated on the 30X Pro MathPrint since the 36X Pro...
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