HP 50g Calculate integral with and without EVAL

[joeres]

Hello everybody,

i would like to know why the EVAL key must be used for the calculation of the integral (https://www.integral-calculator.com/#exp...3&ubound=4): $$\int_{-3}^{4} \left | x^2-4 \right |dx$$If the EVAL key is not used (only key \->NUM), the 50g hangs up and the hourglass is displayed.

The EVAL key is not required to calculate the integral (https://www.integral-calculator.com/#exp...2&ubound=2): $$\int_{-2}^{2} \left | \sin(x) \right |dx$$The result is displayed even if I only use \->NUM.

Maybe someone has an explanation for me?

Thank you and best regards
Joerg

[Joe Horn]

Pressing EVAL on any symbolic expression, when the 50g is in exact mode, performs a SYMBOLIC simplification on it, whereas pressing →NUM (or pressing EVAL when the 50g is in approximate mode) performs a NUMERIC evaluation. These are totally different processes, usually taking different amounts of time to finish (sometimes a LONG time), and often with very different-looking results.

Hint: If a numeric evaluation of an integral takes too long, you can speed it up by setting a smaller display mode, e.g. FIX 4. Your 1st integral evaluates to 23.6649 in 3.8 seconds in FIX 4 mode, and 23.66674 in 14.7 seconds in FIX 5 mode. It's not exact, but numeric methods are always approximate anyway, so it makes sense to limit the accuracy to what you need so as to speed up the process. (If you need exact results, then you must use EVAL in exact mode.)

[joeres]

I understand, thanks for the explanation and the hint.

Joerg