Slow integral evaluation on HP-50g

[cdecastro]

When trying to evaluate the definite integral

int(0,6,abs(2*sin(e^(x/4))+1),x)

on the HP-50. The integration never seems to complete (Regardless of whether I am in approximate or exact mode). Can anyone explain the slow evaluation?

Appreciatively,
Chris

[Manolo Sobrino]

In EMU48 via EQW it works fine and gets this answer (with 10 accurate digits, pay attention to the graph and check if your Number Format is Standard, because then your goal is 12), but only after a little while and using emulation speed. I guess it's Romberg integration, which suffers if the derivatives of the integrand are not continuous, you see that with a small tolerance. Use Approx mode, and change effectively the tolerance via Number Format -> FIX 5, for instance.

When you have an abs function, look if there are points in the interval with a value that could permit two slopes (for a global abs any root will be ). There's the trouble: at some point it won't converge for a subinterval there.

[kakima]

My 50g comes up with an answer of about 12.5733 in STD display after the maximum 64K-1 function evaluations. It comes up with 12.5726 in 4 FIX after only 63 evaluations.

I suspect the noncontinuous derivatives at about x=5.2 has a lot to do with it. Removing the ABS, it comes up with a result after 255 evaluations in STD.