Improper Integrals on 42 platforms

[Thomas Klemm]

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