Integral WP 34S iPad vs Physical Device

[emece67]

After working on this for a while, this integral was a difficult one. In fact even Wolfram alpha fails to compute it and, although the Integral Calculator computes it, it fails if the lower integration limit is changed from \(4\pi\) to \(4.25\pi\). The previous integration program in the wp34s does also fail in such a case.

The problem is that the integrand underflows for all but one sample (and changing the lower integration limit as stated above, it underflows for all sample points).

The number of sample points can be increased, blindly, in the hope for some samples to not underflow. In fact I was able to get correct results this way. But, then, if one tries to integrate the function \(f(x)=0\), the integration time increases dramatically just to return 0 after a long time.

Thus I decided not to modify the algorithm trying to cope with integrands of this kind.

In any case, during the analysis of the problem I've found a bug in the code of the new integration program that caused, in some cases, that the result of the previous iteration being returned instead of the result of the last iteration. I've fixed it and committed it to the SVN repository (now at revision 3900) to be included in the next build.

Regards.