Fractional Part - A Difficult Integral

[pito]

(06-29-2014 06:47 PM)Thomas Klemm Wrote:  

(06-29-2014 06:17 PM)kakima Wrote:  Change the upper limit to 6.4 and try evaluating with the built-in integrator on any HP calculator that has one.

Link for the lazy: Numerical Integration on the 35S.
This is another example where most HP-calculators fail.

Cheers
Thomas

What about to use a simple Monte Carlo method as a "pre-processor" to get a "rough estimate", ie.:

Code:

NIntegrate[x - Floor[x], {x, 0, 6.4}, 
 Method -> {"MonteCarloRule", "Points" -> 1000}]

returns always nice results around 3.08. So we can see whether the specific "precise" integration method with some "difficult" integrands has failed or not..

PS: another example from above posts:

Code:

NIntegrate[
 x*x*(x*x - 47*47)*(x*x - 88*88)*(x*x - 117*117), {x, -128, 128}, 
 Method -> {"MonteCarloRule", "Points" -> 1000}]

gives for example results around 2.72*10^16..