Oddity Using Root Finder with Integrator (long)

[Ben Fairbank]

Parisse --

Thank you for the reply. I do not know how I overlooked the method of restricting an integral to an interval -- now I know. But that was not the real problem.

Consider these two lines:

FNROOT(int(xx^3*(1-xx)^5/Beta(4,6),xx)-.25,xx,0.50)
and
FNROOT(int(xx^(p-1)*(1-xx)^(q-1)/Beta(p,q),xx)-.25,xx,0.50)

They are identical except that one uses the number 5 and the other uses q-1 (q elsewhere given the value of 6, and p = 4). The lines should give the same result if p = 4 and q = 6. Yet the first line succeeds (results in a value of .29) but the second line fails on a Prime with software version 5447, CAS version 1.1.0-27. This peculiar anomaly is stopping a program I have written from running...

Ben Fairbank

(03-13-2014 07:47 AM)parisse Wrote:  Your problem is not well defined, because an integral is defined up to a constant, you should use a integral with boundaries. Should be e.g.
fsolve(int(x^3*(1-x)^5/Beta(4,6),x,0,xx)-.25,xx,.5)
Anyway, I'm unable to reproduce your problem with the latest source build. I get 0.29...
If you want to restrict to an interval, you can enter e.g.
fsolve(int(xx^(p-1)*(1-xx)^(q-1)/Beta(p,q),xx)-.25,xx=-1..1)
then dichotomy is used (and here it will find more than one root), otherwise an iterative Newton-like method is used.