Problem with integral on WP 34s

[Nigel (UK)]

A little more information: the integration routine was changed to the double exponential method in release 3893. To save people poking about in the code, here are the complete comments from the integration code file:

Quote:// Double Exponential Integration for the wp34s calculator
//
// v1.4x-412 (20180312) by M. César Rodríguez GGPL
//
// USAGE:
// Inputs:
// - integration limits in X (upper limit) and Y (lower limit)
// Outputs:
// - approximate value of integral in X
// - estimated error in Y
// - upper integration limit in Z
// - lower integration limit in T
// - updates L (with upper limit)
// - in SSIZE8 mode, all ABCD will be corrupted
//
// Remarks:
// - accepts +Infinite and -Infinite as integration limits. If none
// of the limits is infinite, the method applied is the tanh-sinh
// one. If both are infinite then the sinh-sinh method is selected.
// Otherwise the exp-sinh method is used
// - the program tries to get all displayed digits correct, so
// increasing the number of displayed digits will (hopefully) give
// closer approximations (needing more time). But, in DBLON mode, the
// program ignores the number of displayed digits and does its best
// to get as much correct digits as possible
// - during program execution the succesive aproximations are
// displayed (as with the built-in integration program). Pressing
// [<-] will interrupt the program & the last approximation
// will be returned. The estimated error will be 0 in this case
// - if the computed error estimation is not much smaller than the computed
// result, it is assumed that all digits of the result are corrupted by
// roundoff. In such cases, the reported result is 0 and the reported
// error estimation equals the sum of the absolute values of the computed
// result and error. This usually happens when the integral evaluates to 0
// - if the user has set the D flag, many errors when evaluating the
// integrand (say 0/0 or 1/0, overflows or ...) will not raise an error,
// but return infinite or NaN instead. Such conditions will be detected
// by this program that will continue the computation simply ignoring
// the offending point
// - keep in mind that, when both integration limits are infinite (or
// one is infinite and the other 0) the integrand may be evaluated
// at really bigs/small points (up to 1e±199 in DBLOFF mode and
// 1e±3088 in DBLON mode). Ensure that your integrand program
// behaves as expected for such arguments (you may consider to set
// flag D in some circumstances)
// - the double exponential method relies on the function to be
// integrated being analytic over the integration interval, except,
// perhaps, at the interval ends. Thus, if it is known that the
// integrand, _or any of its derivatives_, has a discontinuity at some
// point inside the integration interval, it is advised to break the
// interval at such point and compute two separate integrals, one
// at each side of the problematic point. Better results will be
// get this way. Thus, beware of abs, fp, ip and such non analytic
// functions inside the integrand program. Other methods (Romberg)
// may behave better in this respect, but, on the other side, the
// double exponential method manages discontinuities (of the
// integrand or its derivatives) at the interval edges better and
// is usually way faster that the Romberg method
// - as many other quadrature methods (Romberg included), the
// double exponential algorithm does not manage well highly
// oscillatory integrands. Here, highly oscillatory means that the
// integrand changes sign many (or infinite) times along the
// integration interval
//
// Method used:
// The algorith used here is adapted from that described in:
// H. Takahasi and M. Mori. "Double Exponential Formulas for Numerical
// Integration." Publications of RIMS, Kyoto University 9 (1974),
// 721-741.
// Another useful reference may be:
// David H. Bailey, Xiaoye S. Li and Karthik Jeyabalan, "A comparison
// of three high-precision quadrature schemes," Experimental
// Mathematics, vol. 14 (2005), no. 3, pg 317-329.
//
// 264 steps
// 16 local registers

Nigel (UK)